SOLUTION: find each product (x-y)(x²-xy+y²)

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Question 118727: find each product
(x-y)(x²-xy+y²)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-y%29%28x%5E2-xy%2By%5E2%29 Start with the given expression



x%28x%5E2-xy%2By%5E2%29-y%28x%5E2-xy%2By%5E2%29 Expand the expression. Remember for something like %28a%2Bb%29%28c%2Bd%2Be%29 it expands to a%28c%2Bd%2Be%29%2Bb%28c%2Bd%2Be%29


%28x%29%2A%281x%5E2%29%2B%28x%29%2A%28-1xy%29%2B%28x%29%2A%281y%5E2%29%2B%28-y%29%2A%281x%5E2%29%2B%28-y%29%2A%28-1xy%29%2B%28-y%29%2A%281y%5E2%29 Distribute


x%5E3-x%5E2y%2Bxy%5E2-yx%5E2%2By%5E2x-y%5E3 Multiply


-y%5E3%2B2xy%5E2-2x%5E2y%2Bx%5E3 Combine like terms



x%5E3-2x%5E2y%2B2xy%5E2-y%5E3 Rearrange the terms



So %28x-y%29%28x%5E2-xy%2By%5E2%29 expands and simplifies to x%5E3-2x%5E2y%2B2xy%5E2-y%5E3.

In other words, %28x-y%29%28x%5E2-xy%2By%5E2%29=x%5E3-2x%5E2y%2B2xy%5E2-y%5E3