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

Mar 12, 2017

See the entire simplification process below:

#### Explanation:

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

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

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

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

We can now group and combine like terms:

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

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

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

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