# How do you simplify (x^2 + x + 4)(2x^2 - x + 1)?

May 3, 2017

See the 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.

$\left(\textcolor{red}{{x}^{2}} + \textcolor{red}{x} + \textcolor{red}{4}\right) \left(\textcolor{b l u e}{2 {x}^{2}} - \textcolor{b l u e}{x} + \textcolor{b l u e}{1}\right)$ becomes:

$\left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{2 {x}^{2}}\right) - \left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{1}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{2 {x}^{2}}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{1}\right) + \left(\textcolor{red}{4} \times \textcolor{b l u e}{2 {x}^{2}}\right) - \left(\textcolor{red}{4} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{4} \times \textcolor{b l u e}{1}\right)$

$2 {x}^{4} - {x}^{3} + {x}^{2} + 2 {x}^{3} - {x}^{2} + x + 8 {x}^{2} - 4 x + 4$

We can now group and combine like terms:

$2 {x}^{4} + 2 {x}^{3} - {x}^{3} + 8 {x}^{2} + {x}^{2} - {x}^{2} + x - 4 x + 4$

$2 {x}^{4} + 2 {x}^{3} - 1 {x}^{3} + 8 {x}^{2} + 1 {x}^{2} - 1 {x}^{2} + 1 x - 4 x + 4$

$2 {x}^{4} + \left(2 - 1\right) {x}^{3} + \left(8 + 1 - 1\right) {x}^{2} + \left(1 - 4\right) x + 4$

$2 {x}^{4} + 1 {x}^{3} + 8 {x}^{2} + \left(- 3\right) x + 4$

$2 {x}^{4} + {x}^{3} + 8 {x}^{2} - 3 x + 4$