# How do you find the product (x^2-4x+5)(5x^2+3x-4)?

Jan 18, 2018

$5 {x}^{4} - 17 {x}^{3} + 9 {x}^{2} + 31 x - 20$

#### Explanation:

$\text{each term in the second factor is multiplied by each term}$
$\text{in the first factor}$

$\Rightarrow \left(\textcolor{red}{{x}^{2} - 4 x + 5}\right) \left(5 {x}^{2} + 3 x - 4\right)$

$= \textcolor{red}{{x}^{2}} \left(5 {x}^{2} + 3 x - 4\right) \textcolor{red}{- 4 x} \left(5 {x}^{2} + 3 x - 4\right)$
$\textcolor{w h i t e}{=} \textcolor{red}{+ 5} \left(5 {x}^{2} + 3 x - 4\right)$

$\text{distribute each bracket and collect like terms}$

$= 5 {x}^{4} + 3 {x}^{3} - 4 {x}^{2} - 20 {x}^{3} - 12 {x}^{2}$+16x
$\textcolor{w h i t e}{=} + 25 {\times}^{2} + 15 x - 20$

$= 5 {x}^{4} - 17 {x}^{3} + 9 {x}^{2} + 31 x - 20$