# What is the standard form of  y= (x-2)(3x+2)(-x+8)?

Dec 10, 2017

$- 3 {x}^{3} + 28 {x}^{2} - 28 x - 32$

#### Explanation:

$\text{expand the first 2 factors using FOIL then multiply the}$
$\text{result by the third factor}$

$\left(x - 2\right) \left(3 x + 2\right) \leftarrow \textcolor{b l u e}{\text{first 2 factors}}$

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

$= 3 {x}^{2} - 4 x - 4$

$\Rightarrow \left(3 {x}^{2} - 4 x - 4\right) \left(- x + 8\right) \leftarrow \textcolor{b l u e}{\text{multiply by third factor}}$

$= - 3 {x}^{3} + 24 {x}^{2} + 4 {x}^{2} - 32 x + 4 x - 32$

$= - 3 {x}^{3} + 28 {x}^{2} - 28 x - 32 \leftarrow \textcolor{b l u e}{\text{in standard form}}$