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Chapter 5: Problem 98

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 the given expression is \(2(y+1)\)

Step by step solution

01

Expand the Expressions

Start with the given expression and distribute \(y+1\) across \((y^{2}-y+1)\) and \((y-1)\) across \((y^{2}+y+1)\). This turns the expression into: \(y^{3}-y^{2}+y+y^{2}-y+1-y^{3}-y^{2}-y+y^{2}+y+1\)
02

Group Like Terms

Next, subtract like terms from each other: \(y^{3}-y^{3}+y^{2}+y^{2}-y^{2}+y-y-y+y+1+1\) which simplifies to \(2y+2\)
03

Factor the Expression

The resultant expression is quite straightforward. But, it is always a good idea to check if you can factor the expression. In this case, the expression can be factored as \(2(y+1)\)

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Most popular questions from this chapter

Explain how to simplify an expression that involves a product raised to a power. Provide an example with your explanation.

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

Explain how to multiply polynomials when neither is a monomial. Give an example.

In each exercise, find the product. $$4 x^{3}\left(4 x^{2}-3 x+1\right)$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. If \(5^{-2}\) is raised to the third power, the result is a number between 0 and 1
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