SOLUTION: Find the product: -9y^2(y^4+8y^3-3y^2+8y+7)

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Question 610654: Find the product: -9y^2(y^4+8y^3-3y^2+8y+7)
Answer by ashipm01(26) About Me  (Show Source):
You can put this solution on YOUR website!
There are two polynomials that are being multiplied: +-9y%5E2+ and +y%5E4+%2B+8y%5E3+-+3y%5E2+%2B+8y+%2B+7+
The first polynomial only has one term, namely +-9y%5E2+
The second polynomial has five terms: y%5E4 8y%5E3 +-3y%5E2+ +8y+ and +7+
So to multiply those two polynomials, take each element in the first polynomial (only one element in this case) and multiply it by each element in the second polynomial. Doing this for this problem will result in a polynomial that has (1 term * 5 terms) = 5 terms.
Performing the multiplication results in the following terms which just need to be summed up after this step:
+-9y%5E2+%2A+y%5E4+ +-9y%5E2+%2A+8y%5E3+ +-9y%5E2+%2A+-3y%5E2+ +-9y%5E2+%2A+8y+ +-9y%5E2+%2A+7+
Summing each of those terms results in the following expression:

Which simplifies to the following:
+-9y%5E6+-+72y%5E5+%2B+27y%5E4+-+72y%5E3+-+63y%5E2+