How to Simplify an Expression: A Beginner's Guide | Algebraic Expressions | Math with Mr. J

In this video, I'm going to cover how to simplify algebraic expressions. I'll cover how to combine like terms and how to use the distributive property in order to do so. We will start with an introduction to combining like terms. Then we will take a look at more examples. After that, we will take a look at an introduction to the distributive property. Following that introduction, we will take a look at more examples. And then lastly, we will simplify expressions by using both combining like terms and the distributive property. Now remember, like terms are terms with the same variables to the same powers. When we combine like terms, we look for any like terms in the given algebraic expression and combine them into one term. By combining like terms, we can simplify expressions. That just means we can rewrite the original expression in a simpler and easier way to understand and work with. Let's jump into number one, where we have 9x plus 3x. We will start with this basic expression and work our way up. So we have two terms in this expression, 9x and 3x. Both terms have the same variable of x, and these variables of x are to the same power. Remember, when we don't have an exponent attached to a variable, there is an understood exponent of 1. Anything to the power of 1 is just itself. So 9x and 3x are like terms. Now when we combine like terms, all we need to do is add or subtract the coefficients, the numbers in front of the variables. The coefficients in number one are 9 and 3. We have a positive 9x plus a positive 3x, so let's add those coefficients. 9 plus 3 is 12, and then we have the variable of x. And that's it. We took those two like terms, 9x and 3x, and combined them into one term, 12x. 12x is equivalent to 9x plus 3x. We didn't change the value of the expression, so 12x is our final simplified expression. Let's move on to number two, where we have 8g plus 7 plus 5g plus 2. Are there any like terms that we can combine in order to simplify this expression? Yes, we have 8g and 5g. Both of those terms have that variable of g. And then we have constant terms, 7 and 2. I'll box in the constant terms to separate them from the 8g and the 5g. Now we can combine like terms. We have 8g plus 5g, that gives us 13g. And then we have 7 plus 2, that gives us 9. So we end up with 13g plus 9, and that's our simplified expression. That expression of 13g plus 9 is equivalent to the original expression. We were just able to simplify the original expression by combining like terms. We started with four total terms, but we were able to combine like terms, and now we only have two total terms. Let's move on to number three, where we have 6y squared plus 10y plus 2y squared plus 3y plus y. Let's find any like terms that we can combine. We'll start with 6y squared. 2y squared is a like term. Both of those terms have that variable of y to the power of 2. Now, do we have any other like terms within this algebraic expression that we can combine? Yes, 10y, and I will box these terms in in order to separate them from the y squared terms. 3y, and then y. Now I do want to mention this term right here, the y, the variable by itself, the coefficient is 1. We don't have a coefficient written in front. Whenever you see that, the coefficient is 1. There is an understood 1 in front of a variable, and it can be helpful to write that 1 in there when you combine like terms. So you can always write that 1 if you would like. Now, since this algebraic expression has five terms, and we are working our way up to more complicated algebraic expressions, we're going to use a strategy to help us organize the expression before we combine like terms. We are going to rearrange and rewrite the expression and put the like terms next to each other. I'll start with 6y squared plus the like term of 2y squared plus, now we have the y terms, so 10y plus 3y plus 1y. So now all of the like terms are next to each other, and it's a little easier to see what we can combine. So this is a strategy to keep in mind. Now, do you have to do this step in order to combine like terms? No, but it can be helpful. Now we can combine like terms. We will start with 6y squared plus 2y squared. So add the coefficients. 6 plus 2 is 8, and then we have y squared plus, now we can combine the y terms. So we have 10 plus 3 plus 1. 10 plus 3 is 13 plus 1 is 14. So we get 8y squared plus 14y. And that's the simplified expression. We now have an equivalent expression that is simpler than the original. We simplified the expression. We went from 5 terms to 2 terms. Let's move on to number 4, where we have 7x plus 2y minus 4x plus 2y. Let's find any like terms that we can combine. We will start with 7x and negative 4x. Now, when we combine like terms, a term is going to take the sign that's in front of it. So this is negative 4x. Then we have 2y and 2y. So let's box those terms in in order to separate them from the x terms. Now we can rewrite this expression with the like terms next to each other. We will start with 7x minus 4x. So we have a negative 4x there. Make sure to bring the sign that's in front of the term with it when we rewrite the expression. Plus 2y. So now we have the y terms plus another 2y. Now we can combine like terms. So we have 7x minus 4x. Or you can think of this as 7x being combined with negative 4x. However you want to think about it. 7 minus 4 is 3. And then we have the x. Or if you're thinking about it as 7x combined with a negative 4x, 7 and negative 4 give us 3 as well. Then we have our 2y plus 2y. That gives us plus 4y. So we end up with 3x plus 4y. And that's our simplified expression. We went from four total terms to two total terms by combining like terms. 3x plus 4y is equivalent to the original expression. We were just able to again simplify this expression by combining like terms. Now I also want to go through simplifying this expression a slightly different way to start off. And that's by rewriting the original expression with only addition separating the terms. We do this by changing any subtraction to adding the opposite. The benefit of having all terms separated only by addition is that it's a little simpler to identify all of the terms. Especially any negative terms. It kind of organizes the expression and helps any negatives stand out. I'll rewrite the expression off to the side here. So 7x plus 2y minus 4x plus 2y. So let's rewrite subtraction as adding the opposite. So adding the opposite of a positive 4x is a negative 4x. So adding the opposite. Let's rewrite the expression with that change. So we have 7x plus 2y plus negative 4x plus 2y. Let's rewrite that expression with like terms next to each other. So 7x plus negative 4x plus 2y plus 2y. Now we can combine like terms. We have 7x plus negative 4x. That gives us 3x. And then we have 2y plus 2y. So that gives us plus 4y. 3x plus 4y that way as well. So that's just another strategy to be aware of. So there's an introduction to combining like terms. Let's take a look at more examples. Here are more examples of algebraic expressions that we will simplify by combining like terms. Let's jump into number one where we have 9c plus 6d plus 5d plus 8c plus 2d. The first thing that we need to do is identify any like terms that we can combine. So are there any like terms that we can combine in this expression? Yes. Let's start with 9c and 8c. Both of those terms have the same variable to the same power. Both terms have the same variable of c to the same understood power of 1. So they are like terms. Remember, when we don't have an exponent attached to a variable, there is an understood exponent of 1. Something is to the power of 1. Anything to the power of 1 is just itself. Do we have any other like terms that we can combine? Yes. We have 6d, 5d, and 2d. All of those terms have the same variable of d to the same understood power of 1. So let's box those terms in in order to separate them from the other terms. Are there any other like terms that we can combine? No. All of the like terms have been identified. So what we can do now, we can rewrite this expression with the like terms next to each other. By rewriting this expression with all of the like terms next to each other, this will help us organize the expression. It will make combining like terms a little simpler. We have 9c plus 8c plus 6d plus 5d plus 2d. So now all of the like terms are next to each other, and it's a little easier to see what we need to combine. So this is a strategy to keep in mind. Do we have to do this step in order to combine like terms? No, but it can be helpful. Now we can combine like terms. Let's start with 9c and 8c. So we have 9c plus 8c. We need to add the coefficients, the numbers in front of the variables. So we have 9 plus 8, which is 17. So we have 17c plus, and now we can combine these terms. So we have 6d plus 5d plus 2d. 6 plus 5 is 11, plus 2 is 13. So we have 13d, and this is our final simplified expression. 17c plus 13d. Now 17c plus 13d is equivalent to the original expression. We went from 5 total terms in the original expression, and simplified it to 2 total terms by combining like terms. Let's move on to number 2, where we have negative 10a plus 2ab plus 9a plus ab plus 9a minus 8. Let's start by identifying any like terms that we can combine. So do we have any like terms that we can combine? Yes, we have negative 10a and 9a and another 9a. All three of those terms have the same variable to the same power. The variable of a to the understood power of 1. Do we have any other like terms that we can combine? Yes, we have 2ab. Let's box these in in order to separate them. And then ab. Now this term right here, ab, does not have a coefficient written in front. Whenever we see this, there is an understood coefficient of 1. So this is 1ab, and we're able to write that 1 in as the coefficient. And it's helpful to do so when combining like terms. That way you know you need to combine that 1. Are there any other like terms within this expression that we can combine? No, but we do have one more term, negative 8. So we have a constant term of negative 8. And I'll circle that term in order to separate it. Even though we don't have anything to combine it with, we still need to include it in the simplified expression. And that is negative 8. Remember, a term will take the sign that's in front of it. We have negative 8 and negative 10a within this expression. Now we can rewrite this expression with the like terms next to each other. We have negative 10a plus 9a plus 9a plus 2ab plus 1ab minus 8. Now we can combine like terms. Let's start with negative 10a plus 9a plus 9a. Negative 10 plus 9 is negative 1 plus 9 is 8, a positive 8. So we have 8a and then plus 2ab plus 1ab. 2 plus 1 is 3. So we have 3ab. And then lastly, we have a negative 8 or minus 8 here. So 8a plus 3ab minus 8 is our final simplified expression. We went from 6 total terms in the original expression to 3 total terms in the simplified expression by combining like terms. Let's move on to numbers 3 and 4, where we actually have the same exact expression. 4x squared minus 7 plus 3x minus 2x squared plus 3. We're going to go through this two slightly different ways. First, we will go through simplifying the expression as it currently is. And that's for number 3. For number 4, we're going to rewrite the expression so all of the terms are separated only by addition. We will talk more about that strategy once we get to number 4. Let's start number 3 by identifying any like terms. So do we have any like terms that we can combine? Yes, we have 4x squared and negative 2x squared. Both of these terms have the same variable of x to the same power of 2. So 4x squared and negative 2x squared. Remember, a term takes the sign that's in front of it. So that's negative 2x squared. Do we have any other like terms that we can combine? Yes, we have two constant terms, negative 7 and 3. I'll box those terms in in order to separate them. And then lastly, we have 3x. We don't have any like terms to combine 3x with, but I will circle it in order to separate it from the other terms. Now we can rewrite this expression with the like terms next to each other. Remember, bring the sign that's in front of the term with it as you rewrite this expression. So we have 4x squared and then negative 2x squared is the like term. So this is going to be 4x squared minus 2x squared. Then we have plus 3x and then our constant terms last. So we have minus 7, a negative 7 plus 3. Now we can combine like terms. We have 4x squared minus 2x squared. Or you can think of this as combining 4x squared and negative 2x squared. However you want to think about it, you'll get the same thing either way. Let's subtract the coefficients. We have 4 minus 2, which gives us 2. Or if you thought about it as 4 combined with negative 2, that gives us 2 as well. So this is 2x squared. Then we have plus 3x and then we can combine negative 7 and 3, positive 3. So we have negative 7 plus 3. That gives us negative 4. So our final simplified expression is 2x squared plus 3x minus 4. We went from 5 total terms in the original expression to 3 total terms by combining like terms. Let's move on to number 4 where we will take a look at a strategy we can use when we have subtraction or negatives involved in the expression. We're going to rewrite the original expression with only addition separating the terms. The benefit of having all terms separated only by addition is that it's a little simpler to identify all of the terms, especially any negative terms. It kind of organizes the expression and helps any negatives stand out. Now do you have to use this strategy? No, but it can be helpful. So I wanted to at least go over it. So let's rewrite this expression with only addition separating the terms. We do this by adding the opposite. So change any subtraction to adding the opposite. Let's change this to addition and then the opposite of positive 7 is negative 7. So add the opposite. Then let's add the opposite here as well. So the opposite of positive 2x squared is negative 2x squared. So let's rewrite this with those changes. So we have 4x squared plus negative 7 plus 3x plus negative 2x squared plus 3. So now all of the terms are separated only by addition. Now we can identify any like terms. We have 4x squared and negative 2x squared. Then we have negative 7 and 3 and then 3x. Now let's rewrite this expression with the like terms next to each other. So we have 4x squared plus negative 2x squared plus 3x plus negative 7 plus 3. Now we can combine like terms. We have 4x squared plus negative 2x squared or plus negative 2 is 2. So we have 2x squared plus 3x plus negative 7 plus 3. Negative 7 plus 3 is negative 4. So plus negative 4. Now this is correct but we can clean this up a little bit so to speak. We have a double sign. We are adding a negative. Adding a negative 4. Adding a negative 4 is the same as subtracting 4. We are decreasing in value by 4. So we can rewrite this with just one sign. We don't need both of those signs. When we add a negative that's the same as just subtracting a positive. So let's change this to subtracting 4. And again getting rid of the double sign will make this a little simpler. It will clean it up. We can rewrite this as 2x squared plus 3x minus 4. And that's our final simplified expression. So you can see that we got the same exact simplified expression for number 3 and 4. Just slightly different strategies as far as organizing the expression to start. Now I do want to mention one last thing and it's about writing out expressions. When we write an expression we typically want any exponents first. If there are multiple exponents write them from greatest to least. If we have the same exponent go in abc order. And then constant terms always come last. So for example in number 1 we have the variables of c and d. Both are to the understood power of 1. So we go in abc order. For number 2 we have a and ab. Everything here is to the understood power of 1. So we go in abc order. a comes first then ab and then the constant term comes last. For numbers 3 and 4 we have x squared. So the greatest exponent 2. Then we have the variable of x to the understood power of 1. And then lastly we have the constant term. So something to keep in mind when you are writing expressions. So there's how to combine like terms. Let's move on to the distributive property. Here is an introduction to the distributive property. Now the distributive property can help us remove parentheses within algebraic expressions. This helps us simplify expressions when we do not have like terms within parentheses that we can combine. Now remember when we have something next to parentheses that means multiplication. So we can use the distributive property to distribute whatever is on the outside of the parentheses to the terms inside the parentheses. The distributive property works when we have addition or subtraction inside of the parentheses. So at the top of the screen there is a general overview of the distributive property where a is being distributed to the terms inside of the parentheses. The distributive property and that overview will make a lot more sense as we go through our examples. Let's jump into number 1 where we have 2 and then in parentheses 5 plus 3. And we're going to do this two different ways by using the order of operations. So doing what's in the parentheses first and then also using the distributive property. Now for number 1 we don't have any variables involved. We are actually able to add what's in the parentheses first and then go from there. We don't have to use the distributive property. But the point of number 1 is to show us that we get the same thing either way. This is going to show us that the distributive property doesn't change the value of an expression. We are able to use this strategy. So again we get the same thing either way. Let's start by using the order of operations and doing what's in the parentheses first. We have 5 plus 3 which is 8. Bring down the 2 and now we have 2 times 8 which is 16. Now let's use the distributive property and see if we still get 16. So we need to take that 2 on the outside of the parentheses and distribute it to the 5 and to the 3. So we have 2 times 5 plus 2 times 3. 2 times 5 gives us 10 plus 2 times 3 gives us 6. 10 plus 6 is 16. So we get 16 that way as well. So we can see that the distributive property doesn't change the value of an expression. And we are able to use it. Let's move on to number 2 where we will apply this to an algebraic expression. In order to simplify the expression we are going to remove the parentheses. For number 2 we have 8 and then in parentheses 2m plus 6. Now we can't combine those terms in the parentheses. So what we can do we can use the distributive property to remove those parentheses and simplify this expression. So let's distribute the 8 to the 2m and to the 6. This gives us 8 times 2m plus 8 times 6. 8 times 2m is 16m plus 8 times 6 is 48. Now 16m and 48 are unlike terms. So we don't have any terms that we can combine. So we are done here. 16m plus 48 is our simplified expression. Let's move on to number 3 where we have 7 and then in parentheses a minus 9. Let's distribute that 7 to the a and to the 9. That gives us 7 times a minus, bring the subtraction sign down, 7 times 9. 7 times a is just 7a minus 7 times 9 is 63. So we end up with 7a minus 63. We don't have any like terms that we can combine. So we are simplified and done. Again 7a minus 63. Now I do want to mention another way to think through this and this is another way to think through whenever subtraction or negatives are involved. So let me rewrite the expression and then distribute the 7. So we have 7 times a which is 7a and then we can think of that subtraction sign and the 9 as a negative 9. So including the sign in front with the 9. So we think of that as a negative 9. So let's distribute that 7 to the negative 9. 7 times negative 9 is negative 63. So negative 63. And we get 7a minus 63 that way as well. And again that's just a different way to think through it. You get the same thing either way but you can include the sign in front of the term and think of that as a negative 9. So something to keep in mind. Let's move on to number 4 where we have 10 and then in parentheses negative 5x minus 4y. Let's distribute the 10 to the negative 5x and to the 4y. So 10 times negative 5x minus 10 times 4y. 10 times negative 5x gives us negative 50x minus 10 times 4y gives us 40y. So we end up with negative 50x minus 40y. We don't have any like terms that we can combine. So we are done. Again negative 50x minus 40y. Now let's take a look at a different way to think through this. So I will rewrite the expression off to the side. So let's distribute the 10 to the negative 5x and then we will think of that as negative 4y. So include the sign in front of that term. 10 times negative 5x is negative 50x and then 10 times negative 4y is negative 40y. So we get the same thing that way as well. Negative 50x minus 40y. So there is an introduction to the distributive property. Let's take a look at 4 more examples. Here are more examples that we can go through to get the distributive property down. Let's jump into number 1 where we have 9 and then 3c plus 2 in the parentheses. Let's distribute that 9 to the 3c and to the 2. So we have 9 times 3c which is 27c plus. So we bring that addition sign down and then we have 9 times 2 which is 18. So we end up with 27c plus 18. Now we don't have any like terms that we can combine. So this has been simplified. We can't simplify any further. So again 27c plus 18. Let's move on to number 2 where we have 4 and then in parentheses negative 6y minus 5. Let's distribute that 4 to the negative 6y and to the 5. So 4 times negative 6y is negative 24y. Bring the subtraction sign down and then we have 4 times 5 which is 20. So we end up with negative 24y minus 20. We don't have any like terms that we can combine. So this is simplified. Again negative 24y minus 20. Now I do want to mention another way to think through number 2 and this is an option when we have subtraction. So let me rewrite the expression here and then we need to distribute the 4. So distribute to the negative 6y and then when we distribute to the 5 we are going to look at this as negative 5. So we are including that subtraction sign the sign in front of the 5 and look at this as negative 5. This gives us well 4 times negative 6y is negative 24y and then 4 times negative 5 is negative 20. So we get negative 24y minus 20 that way as well. We get the same thing either way just slightly different as far as working through the distributive property. Let's move on to number 3 where we have negative 2 and then in parentheses negative 8x minus 7y. Let's distribute the negative 2 to the negative 8x and to 7y. So negative 2 times negative 8x gives us 16x. Remember a negative times a negative is a positive so negative 2 times negative 8 is a positive 16 and then we have that x. Then we can bring down the subtraction sign and then we have negative 2 times 7y that gives us negative 14y. Now this is correct but we can clean this up a little bit so to speak. We have a double sign the subtraction and then the negative. We don't need both of those signs we can rewrite it with just one. Think about working with negatives. When we subtract a negative that's the same as adding a positive. We can change this to addition and that will make this simpler and like I said clean it up a little bit. We can rewrite this as 16x plus 14y. We don't have any like terms that we can combine so we are simplified again 16x plus 14y. Just like number 2 I'll go through this a slightly different way as far as thinking through the distributive property when it comes to subtraction. I will rewrite the expression off to the side here and then we can distribute that negative 2 to the negative 8x and then we can distribute that negative 2 to the negative 7y so we are including that sign in front of the term. Negative 2 times negative 8x gives us 16x and then negative 2 times negative 7y gives us a positive 14y so plus 14y so we get the same thing there as well. Lastly let's move on to number 4 where we have 15 and then 3g plus h in the parentheses so let's distribute that 15 to the 3g and to the h so we have 15 times 3g that gives us 45g plus and then 15 times h well that's just 15h so we end up with 45g plus 15h. We don't have any like terms that we can combine so we can't simplify this any further this is simplified so again 45g plus 15h so there are the basics of using the distributive property to simplify algebraic expressions. Let's move on to some examples of algebraic expressions that will need to be simplified using both the distributive property and combining like terms. Here are four more algebraic expressions that we need to simplify. We will use both the distributive property and combining like terms. Let's jump into number 1 where we have 4 plus 2 and then in parentheses n plus 6. Now since this expression has parentheses we need to start there. Do not do 4 plus 2 first. We still need to consider the order of operations. Within the parentheses we have n plus 6. n and 6 are unlike terms so we can't combine those terms. What we can do is use the distributive property to remove the parentheses and then we can look to combine like terms to simplify the expression further. So let's distribute the 2 to the n and to the 6. 2 times n gives us 2n and then we have 2 times 6 which gives us a positive 12 so plus 12. This is a positive 2n and then we can bring down that 4. Now that the parentheses have been removed we can look to simplify further by combining like terms. 4 and 12 are like terms. Those are constant terms so we can combine them. 4 plus 12 gives us 16 so our final simplified expression is 2n plus 16. Now when we write expressions typically speaking we want any variable terms first and then constant terms go last. So that's why we have 2n plus 16. If we end up having multiple terms that involve variables they go in order from greatest to least as far as exponents and then if variable terms have the same exponents go in abc order. So again for number 1 we just have two terms a variable term and then a constant term. So 2n plus 16 is our final simplified expression. Now that final simplified expression is equivalent to the original expression. We were just able to simplify that original expression by using the distributive property and combining like terms. Let's move on to number 2 where we have 6 and then in parentheses 3x plus 5 and parentheses minus 9x. Let's start by using the distributive property to remove the parentheses. So let's distribute this 6 to the 3x and to the 5. 6 times 3x gives us 18x and then 6 times 5 gives us a positive 30 so plus 30. Then we have minus 9x so a negative 9x. Now that we removed the parentheses we can look to combine like terms. 18x and negative 9x are like terms so we can combine them. Make sure to include the sign that's in front of a term that's negative 9x. So we have 18x minus 9x or 18x combined with negative 9x. That gives us a positive 9x and then we have plus 30 a positive 30. So our final simplified expression is 9x plus 30. Let's move on to number 3 where we have 23 plus 3 and then in parentheses 8y minus 10. Let's remove the parentheses by using the distributive property. So let's distribute the 3 to the 8y and to the negative 10. 3 times 8y gives us 24y and then 3 times negative 10 gives us negative 30. This is a positive 24y and then bring down the 23. Now as far as the distributive property and subtraction we can also think through that as 3 times 8y that gives us 24y. Then we can bring the subtraction sign down and then distribute the 3 to the 10. So 3 times 10 that gives us 30. So 24y minus 30. We got the same thing thinking through the distributive property that way as well. Now that we removed the parentheses we can look to combine like terms. We have two constant terms 23 and negative 30. So we can combine those like terms. So we have 24y and then 23 minus 30 or 23 combined with negative 30 gives us negative 7. So minus 7. Our final simplified expression 24y minus 7. Lastly let's move on to number 4 where we have negative 8 and then in parentheses negative c minus d and parentheses minus 5d. Let's start by removing the parentheses by using the distributive property. Distribute the negative 8 to the negative c and distribute the negative 8 to negative d. Negative 8 times negative c gives us a positive 8c. Remember a negative times a negative equals a positive. Negative 8 times negative d gives us a positive 8d and then we have minus 5d. So a negative 5d. Now that we removed the parentheses we can look to combine like terms. 8d and negative 5d are like terms. So let's combine those like terms. We end up with 8c and then 8d minus 5d or 8d combined with negative 5d gives us a positive 3d. So plus 3d. Our final simplified expression 8c plus 3d. So there's how to use the distributive property and combining like terms to simplify an algebraic expression. Let's take a look at four more examples and these will get a little more complex. Here are four more algebraic expressions that we need to simplify using the distributive property and combining like terms. These will get a little more complex than the previous four examples. Let's jump into number one where we have 13a plus 4 and then in parentheses a plus 9. Now since we have parentheses we need to start there. We can't combine the terms in the parentheses. They are unlike terms. So we can use the distributive property to remove the parentheses. Once the parentheses are removed we can look to combine like terms. So let's distribute that 4 to the a and to the 9. So we have 4 times a which is 4a and then 4 times 9 is a positive 36. So plus 36. This is a positive 4a and then we can bring down 13a. Now that we removed the parentheses we can look to combine like terms in order to simplify this further. So do we have any like terms that we can combine? Yes. 13a and 4a are like terms. So we can combine those terms. 13a plus 4a is 17a and then we have that positive 36. So plus 36 and this is our final simplified expression. 17a plus 36. Now that simplified expression is equivalent to the original expression. We were just able to simplify that original expression by using the distributive property and combining like terms. Let's move on to number 2 where we have 5 and then in parentheses x squared minus 3 and parentheses plus 10 minus 4x. Let's start by using the distributive property in order to remove the parentheses. Then we can look to combine like terms. Let's distribute this 5 to the x squared and to the negative 3. 5 times x squared gives us 5x squared and then 5 times negative 3 gives us negative 15. Now another way to think through that distributive property there is to do 5 times x squared which is 5x squared bring the subtraction sign down and then do 5 times 3. We get 5x squared minus 15 that way as well. Just a slightly different way to think through the distributive property. Then we have a positive 10. So plus 10 and then a negative 4x. So minus 4x. Now that we removed the parentheses we can look to combine like terms. So do we have any like terms that we can combine? Yes we have two constant terms negative 15 and 10. So let's combine those like terms. So we have 5x squared minus 4x. That's a negative 4x. The term will take the sign that's in front of it. So make sure we have negative 4x there and then the constant term comes last. So we have negative 15 plus 10 or negative 15 combined with positive 10. That gives us negative 5. So minus 5. And this is our final simplified expression. 5x squared minus 4x minus 5. Now I do want to mention as far as how this simplified expression is written. Typically speaking when writing expressions the greatest exponent comes first. So greatest to least. If exponents are the same go in abc order. Constant terms go last. So we have 5x squared. The exponent of 2 comes first because that's the greatest exponent. Then we have negative 4x. So that variable has an understood exponent of 1. Remember whenever there isn't an exponent written there is an understood exponent of 1. So to the power of 1. Anything to the power of 1 is just itself. And then we have the constant term of negative 5 last. So that's something to keep in mind as far as writing out expressions. Let's move on to number 3 where we have 7 and then in parentheses g plus 3h and parentheses plus 4 and then in parentheses 2g minus 6h. Let's start by using the distributive property to remove any parentheses. And then we can look to combine like terms. Let's distribute this 7 to the g and to the 3h. So we have 7 times g. That gives us 7g. And then we have 7 times 3h. That gives us a positive 21h. So plus 21h. Then we can distribute the 4 to the 2g and to the negative 6h. 4 times 2g gives us a positive 8g. So plus 8g. And then 4 times negative 6h gives us negative 24h. A positive times a negative equals a negative. So negative 24h or minus 24h. Now for this expression, I'm going to rewrite it with all of the like terms next to each other. This is a strategy we can use to organize the expression and make combining like terms a little simpler since all of the like terms will be right next to each other. So let's identify any like terms in this expression. We have 7g and 8g. And then 21h which I will box in in order to separate. And then negative 24h. Let's rewrite this with those like terms next to each other. So we have 7g plus 8g plus 21h minus 24h. Remember that's a negative 24h. Now all of the like terms are right next to each other. So like I mentioned, it's a little simpler to combine the like terms. So now we can combine like terms. Let's start with 7g and 8g. 7g plus 8g gives us 15g. Then we have 21h minus 24h. So positive 21h combined with negative 24h. That gives us negative 3h. So minus 3h. And this is our final simplified expression. 15g minus 3h. Lastly, let's move on to number 4 where we have 18x minus 10 and then in parentheses 2x minus 2y plus 9 and parentheses minus 6x. Let's start by using the distributive property to remove the parentheses. We're going to distribute negative 10. We take the sign that's in front. So this is negative 10. We need to distribute to the 2x to the negative 2y and to the 9. Negative 10 times 2x gives us negative 20x. Negative 10 times negative 2y gives us positive 20y. Remember a negative times a negative equals a positive. And then we have negative 10 times a positive 9. That gives us negative 90. We then have the negative 6x and the positive 18x that we need to bring down. Now we can look for any like terms that we can combine. So do we have any like terms? Yes. 18x, negative 20x, and negative 6x. Let's rewrite the expression with those like terms next to each other. So 18x minus 20x minus 6x plus 20y minus 90. Now we can combine like terms. So we have 18x minus 20x minus 6x. So we are combining a positive 18x, a negative 20x, and a negative 6x. 18x minus 20x is negative 2x. Negative 2x minus 6x, that gives us negative 8x. Then we have plus 20y minus 90. So negative 8x plus 20y minus 90 is our final simplified expression. So there's how to simplify algebraic expressions by combining like terms and using the distributive property. I hope that helped. Thanks so much for watching. Until next time, peace.