Difference of Squares
Now let’s look at a second case.
This second case is another special product, but instead of being the same sign they are going to be opposite signs.
You have (x-4)(x+4) let’s foil this problem out. First times first, which equals x times x is x^2, outer, x times 4 which is 4x, and inner which is negative 4 times 4 is -4x, and last is -4x4 = negative16. What do notice about the middle terms and we had one of these in the last lesson. The signs are opposite so they will cancel each other out because +4 and -4 is zero, so you are left with x^2 and back here you have -16 This is called the difference of two squares. We have two perfect squares. We have x^2 is a perfect square, and 16 is a perfect square, and difference means subtraction. When you multiply these together you will end up with a binomial answer. Let’s look at (2z-5)(2z+5) and see what happens with it. (2z-5)(2z+5) so multiply first which equals 4z^2,outer which is 10Z inner is positive 10z and we can see these will be gone, and -5 x5 = -25 Be careful with the sign and we bring down a 4z^2 and -25 and that is the special product of the difference of two squares. Now let’s look at number 6 (4r+7y)(4r-7) try that and see what you get. Pause the video or keep watching I'm going to write out the answer. Does the order of this product matter? No because order doesn't matter, think of 3x4 and 4x3 you get the same product with both. First,outer,inner,and last. I can cross these out and I get 16r^2-49y^2 which is difference of two squares. 16 and 49 are both perfect square numbers
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