An Intro to the Distributive Property | Simplifying Expressions | Math with Mr. J

welcome to math with Mr Jay [Music] in this video I'm going to go through an introduction to simplifying algebraic expressions using 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 just jump into number one where we have two and then in parentheses five plus three 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 one 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 one 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 five plus three which is eight bring down the two and now we have two times eight 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 two times five plus two times three two times five 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 two where we will apply this to an algebraic expression in order to simplify the expression we are going to remove the parentheses for number two we have 8 and then in parentheses 2m plus six 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 eight times six eight times two m is 16 M plus eight times six is Forty-Eight now 16 M 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 three where we have 7 and then in parentheses a minus 9. let's distribute that 7 to the A and to the nine that gives us 7 times a minus bring the subtraction sign down 7 times 9. 7 times a is just seven a minus seven times nine 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 nine so we think of that as a negative nine so let's distribute that 7 to the negative nine seven times negative nine 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 four 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 4 y 10 times negative 5x gives us negative 50 x minus 10 times 4y gives us 40 y 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 50 x 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 you have it there's an introduction to the distributive property check the description for a link to Part 2 where I go through four more examples I hope that helped thanks so much for watching until next time peace you know