SOLUTION: Multiply {{{(s+p)(s^2-sp+p^2)}}}

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Question 131915: Multiply %28s%2Bp%29%28s%5E2-sp%2Bp%5E2%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28s%2Bp%29%28s%5E2-sp%2Bp%5E2%29 Start with the given expression



s%28s%5E2-sp%2Bp%5E2%29%2Bp%28s%5E2-sp%2Bp%5E2%29 Expand the expression. Remember something like %28a%2Bb%29%28c%2Bd%2Be%29 expands to a%28c%2Bd%2Be%29%2Bb%28c%2Bd%2Be%29


Distribute


s%5E3-s%5E2p%2Bsp%5E2%2Bps%5E2-p%5E2s%2Bp%5E3 Multiply


s%5E3%2Bps%5E2-ps%5E2%2Bp%5E2s-p%5E2s%2Bp%5E3 Rearrange the terms


s%5E3%2Bcross%28ps%5E2-ps%5E2%29%2Bcross%28p%5E2s-p%5E2s%29%2Bp%5E3 Combine like terms. Notice how the inner terms cancel out


s%5E3%2Bp%5E3 Simplify



So %28s%2Bp%29%28s%5E2-sp%2Bp%5E2%29 expands and simplifies to s%5E3%2Bp%5E3.

In other words, %28s%2Bp%29%28s%5E2-sp%2Bp%5E2%29=s%5E3%2Bp%5E3