SOLUTION: y=(x+5)(x²+3x+4)

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Question 1198618: y=(x+5)(x²+3x+4)
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I assume you want to expand that out. In the future, please post the verbal instructions.

y+=+%28x%2B5%29%28x%5E2%2B3x%2B4%29

y+=+w%28x%5E2%2B3x%2B4%29 Let w = x+5

y+=+wx%5E2%2B3wx%2B4w Distribute

y+=+x%5E2%28w%29%2B3x%28w%29%2B4%28w%29

y+=+x%5E2%28x%2B5%29%2B3x%28x%2B5%29%2B4%28x%2B5%29 Plug in w = x+5

y+=+%28x%5E3%2B5x%5E2%29%2B%283x%5E2%2B15x%29%2B%284x%2B20%29 Distribute three times more

y+=+x%5E3%2B8x%5E2%2B19x%2B20 Combine like terms

Therefore,
%28x%2B5%29%28x%5E2%2B3x%2B4%29+=+x%5E3%2B8x%5E2%2B19x%2B20
is an identity, i.e. it is a true equation for all real numbers x.