# How do you simplify (x - 1)(x^3 + 2x^2 + 2)?

Jul 1, 2018

See a solution process below:

#### Explanation:

To simplify these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{x} - \textcolor{red}{1}\right) \left(\textcolor{b l u e}{{x}^{3}} + \textcolor{b l u e}{2 {x}^{2}} + \textcolor{b l u e}{2}\right)$ becomes:

$\left(\textcolor{red}{x} \times \textcolor{b l u e}{{x}^{3}}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{2 {x}^{2}}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{2}\right) - \left(\textcolor{red}{1} \times \textcolor{b l u e}{{x}^{3}}\right) - \left(\textcolor{red}{1} \times \textcolor{b l u e}{2 {x}^{2}}\right) - \left(\textcolor{red}{1} \times \textcolor{b l u e}{2}\right)$

${x}^{4} + 2 {x}^{3} + 2 x - {x}^{3} - 2 {x}^{2} - 2$

We can now group and combine like terms:

${x}^{4} + 2 {x}^{3} - {x}^{3} - 2 {x}^{2} + 2 x - 2$

${x}^{4} + 2 {x}^{3} - 1 {x}^{3} - 2 {x}^{2} + 2 x - 2$

${x}^{4} + \left(2 - 1\right) {x}^{3} - 2 {x}^{2} + 2 x - 2$

${x}^{4} + 1 {x}^{3} - 2 {x}^{2} + 2 x - 2$

${x}^{4} + {x}^{3} - 2 {x}^{2} + 2 x - 2$