Problem 15 - College Algebra

Question

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

Step-by-Step Solution

Answer

The product of \( (x + 1) \) and \( (x^2 - x + 1) \) is \(x^3 + 1\).

Step 1: Distributing First Term

Multiply the first term in the first polynomial (which is \(x\)) with each term in the second polynomial. This gives: \(x * x^2\), \(x * -x\), \(x * 1\) which simplify to \(x^3\), \(-x^2\), \(x\).

Step 2: Distributing Second Term

Next, multiply the second term in the first polynomial (which is \(1\)) with each term in the second polynomial. That gives: \(1 * x^2\), \(1 * -x\), \(1 * 1\) which simplify to \(x^2\), \(-x\), \(1\).

Step 3: Combine Like Terms

Finally, we combine like terms from the outcomes of step 1 and step 2 to get the final expression. This results in: \(x^3 - x^2 + x + x^2 - x + 1\). Combining the like terms gives: \(x^3 + 1\).