Ein mega hilfreicher Kopfrechentrick!

In this video, I'll show you a head count trick and why it works. I want to multiply two numbers, 39 and 41. There are different head count strategies that you can use. 30 times 41 plus 9 times 41. Or you calculate 40 times 41 and subtract 41. Or 39 times 40 plus 39 times 1. There are different strategies and everyone has the potential to calculate. I'll show you a trick to make it easier in this case. The trick always works very well when the number in the middle between these two numbers is easy to square. I'll draw it on the right. I have 39 and 41 here. Which number is exactly in the middle? The 40. The 40 is relatively easy to square. I square the 40 and subtract the distance from which the 40 of the two numbers has. Here the distance is 1. Minus 1 square. This is also relatively easy. I just have to calculate 1,600 minus 1. 1,599. So 39 times 41 is 1,599. Another example. 67 times 73. If I want to calculate that, I look again at the head count. Which number is exactly in the middle between 67 and 73? Is it easy to square? There is the 70. Yes, it is easy to square. So I calculate 70 square minus the distance from the 70 to the two numbers, which is 3. So minus 3 square. 70 square is 4,900. 3 square is 9. 4,900 minus 9 is 4,891. So, I want to multiply two numbers together. Looks relatively difficult. The number in the middle is relatively easy to square. The distance is easy to square. Then I take the number in the middle to the square. Minus distance square. And I get the result. Why does this work? This is relatively easy to prove. With the help of the third binomial formula. I have two numbers that I want to multiply with each other. x times y. Here is x and there is y. Now there is a number in the middle. Let's call it a. And a is exactly the same distance from x and y with the distance b. So x is nothing other than a minus b. And y is nothing other than a plus b. We can write that in here. x times y is the same as a minus b times a plus b. So the number in the middle, once the distance subtracted, once added. a minus b times a plus b. And this is the third binomial formula. This is a square minus b square. So just the number in the middle. a to the square, just the number in the middle. minus b square. So minus the distance to the square. Maybe you have similar math tricks? Write it in the comments.