# How do you simplify (x^2 - x - 3)(x^2 + 4x + 2)?

Apr 29, 2017

See the entire solution 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.

$\left(\textcolor{red}{{x}^{2}} - \textcolor{red}{x} - \textcolor{red}{3}\right) \left(\textcolor{b l u e}{{x}^{2}} + \textcolor{b l u e}{4 x} + \textcolor{b l u e}{2}\right)$ becomes:

$\left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{{x}^{2}}\right) + \left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{4 x}\right) + \left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{2}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{4 x}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{2}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{4 x}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{2}\right)$

${x}^{4} + 4 {x}^{3} + 2 {x}^{2} - {x}^{3} - 4 {x}^{2} - 2 x - 3 {x}^{2} - 12 x - 6$

We can now group and combine like terms:

${x}^{4} + 4 {x}^{3} - {x}^{3} + 2 {x}^{2} - 4 {x}^{2} - 3 {x}^{2} - 2 x - 12 x - 6$

${x}^{4} + 4 {x}^{3} - 1 {x}^{3} + 2 {x}^{2} - 4 {x}^{2} - 3 {x}^{2} - 2 x - 12 x - 6$

${x}^{4} + \left(4 - 1\right) {x}^{3} + \left(2 - 4 - 3\right) {x}^{2} + \left(- 2 - 12\right) x - 6$

${x}^{4} + 3 {x}^{3} + \left(- 5\right) {x}^{2} + \left(- 14\right) x - 6$

${x}^{4} + 3 {x}^{3} - 5 {x}^{2} - 14 x - 6$