# How do you multiply (x-4)(x^2-5x+3)?

Mar 31, 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.

$\left(\textcolor{red}{x} - \textcolor{red}{4}\right) \left(\textcolor{b l u e}{{x}^{2}} - \textcolor{b l u e}{5 x} + \textcolor{b l u e}{3}\right)$ becomes:

$\left(\textcolor{red}{x} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{5 x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{3}\right) - \left(\textcolor{red}{4} \times \textcolor{b l u e}{{x}^{2}}\right) + \left(\textcolor{red}{4} \times \textcolor{b l u e}{5 x}\right) - \left(\textcolor{red}{4} \times \textcolor{b l u e}{3}\right)$

${x}^{3} - 5 {x}^{2} + 3 x - 4 {x}^{2} + 20 x - 12$

We can now group like terms:

${x}^{3} - 5 {x}^{2} - 4 {x}^{2} + 3 x + 20 x - 12$

We can now combine like terms:

${x}^{3} + \left(- 5 - 4\right) {x}^{2} + \left(3 + 20\right) x - 12$

${x}^{3} + \left(- 9\right) {x}^{2} + 23 x - 12$

${x}^{3} - 9 {x}^{2} + 23 x - 12$

Mar 31, 2017

color(blue)(x^3-9x^2+23x-12

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$${x}^{2} - 5 x + 3$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$x - 4$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- - - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$${x}^{3} - 5 {x}^{2} + 3 x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a}$$- 4 {x}^{2} + 20 x - 12$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- - - - - - - - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$color(blue)(x^3-9x^2+23x-12