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Chapter 5: Problem 96

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 form of \((y+1)(y^{2}-y+1)-(y-1)(y^{2}+y+1)\) is \(y^{3} + 2\).

Step by step solution

01

Expand the Polynomials

Expand both polynomials by distributing the terms in the parentheses: \[ y^{3} + y^{2} + y + y^{2} - y + 1 \] for the first polynomial and \[ y^{3} + y^{2} + y - y^{2} - y - 1\] for the second polynomial.
02

Simplify the Polynomials

Combine like terms for both polynomials: the first polynomial simplifies to \(2y^{3} + 2\), and the second polynomial simplifies to \(y^{3}\).
03

Subtract the Second Polynomial from the First

Subtract the second polynomial from the first to get: \(2y^{3} + 2 - y^{3} = y^{3} + 2 \)

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