Problem 15 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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: \(x^{3} - x^{2} + x\).

Step 2: 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: \(x^{2} - x + 1\).

Step 3: 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 \(x^{3}\).