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Chapter 5: Problem 97

Perform the indicated operations. $$(y+1)\left(y^{2}-y+1\right)+(y-1)\left(y^{2}+y+1\right)$$

Short Answer

Expert verified
The simplified expression of \((y+1)(y^{2}-y+1)+(y-1)(y^{2}+y+1)\) is \(2y^{3} + 1\).

Step by step solution

01

Expand the Product of Binomials

First, expand the product of binomials by applying the distributive property which states a(b + c) = ab + ac. Hence, we get: \(y^{3} - y^{2} + y + y^{2} - y + 1 + y^{3} + y^{2} + y - y^{2} - y - 1\)
02

Combine Like Terms

Next, combine like terms to simplify the expression further. When you combine like terms, you will end up with: \(2y^{3} + 1\)

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