SOLUTION: (2r-3s)(4r^2+6rs+9s^2)

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Question 112005: (2r-3s)(4r^2+6rs+9s^2)
Answer by jim_thompson5910(28595) About Me  (Show Source):
You can put this solution on YOUR website!

%282r-3s%29%284r%5E2%2B6rs%2B9s%5E2%29 Start with the given expression



2r%284r%5E2%2B6rs%2B9s%5E2%29-3s%284r%5E2%2B6rs%2B9s%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


Distribute


8r%5E3%2B12rs%2B18rs%5E2-12sr%5E2-18s%5E2r-27s%5E3 Multiply


8r%5E3%2B12rs-12r%5E2s-27s%5E3 Combine like terms


8r%5E3-12r%5E2s%2B12rs-27s%5E3 Sort the terms



So %282r-3s%29%284r%5E2%2B6rs%2B9s%5E2%29 expands and simplifies to 8r%5E3-12r%5E2s%2B12rs-27s%5E3.

In other words, %282r-3s%29%284r%5E2%2B6rs%2B9s%5E2%29=8r%5E3-12r%5E2s%2B12rs-27s%5E3