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Chapter 0: Problem 15

Find each product. $$(x+1)\left(x^{2}-x+1\right)$$

Short Answer

Expert verified
\The product is \(x^{3}\).

Step by step solution

01

Distribute \(x\) from the first set of parentheses

Multiply the \(x\) from the first parentheses to each term of the second parentheses. This would be: \(x*x^{2}\) which equals to \(x^{3}\), \(x*-x\) equals to \(-x^{2}\) and \(x*1\) which equals \(x\). So you get: \(x^{3} - x^{2} + x\).
02

Distribute \(1\) from the first set of parentheses

Next multiply the \(1\) from the first parentheses to each term of the second parentheses. This would be: \(1*x^{2}\) which equals to \(x^{2}\), \(1*-x\) equals to \(-x\) and \(1*1\) which equals \(1\). So you obtain: \(x^{2} - x + 1\).
03

Combine like terms

Now combine like terms from step 1 and step 2. Like terms are terms that have the same variable and exponent. This yields: \(x^{3} - x^{2} + x + + x^{2} - x + 1\), which simplifies to \(x^{3}\).

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