# How do you simplify the product (x + 6)(x^2 - 4x + 3)  and write it in standard form?

Jul 5, 2017

See a 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.

$\left(\textcolor{red}{x} + \textcolor{red}{6}\right) \left(\textcolor{b l u e}{{x}^{2}} - \textcolor{b l u e}{4 x} + \textcolor{b l u e}{3}\right)$ becomes:

$\left(\textcolor{red}{x} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{4 x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{3}\right) + \left(\textcolor{red}{6} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{4 x}\right) + \left(\textcolor{red}{6} \times \textcolor{b l u e}{3}\right)$

${x}^{3} - 4 {x}^{2} + 3 x + 6 {x}^{2} - 24 x + 18$

Next, group like term in descending order by the power of there exponents:

${x}^{3} + 6 {x}^{2} - 4 {x}^{2} + 3 x - 24 x + 18$

We can now combine like terms:

${x}^{3} + \left(6 - 4\right) {x}^{2} + \left(3 - 24\right) x + 18$

${x}^{3} + 2 {x}^{2} + \left(- 21\right) x + 18$

${x}^{3} + 2 {x}^{2} - 21 x + 18$