# What is the standard form of y= (4x)(x-3)-(x^2-4)(-x+2) ?

Dec 20, 2015

$y = - {x}^{3} + 2 {x}^{2} - 16 x + 8$

#### Explanation:

The standard form of a general equation of degree $3$ is
$\textcolor{w h i t e}{\text{XXX}} y = a {x}^{3} + b {x}^{2} + c x + d$

To convert the given equation: $y = \textcolor{red}{\left(4 x\right) \left(x - 3\right)} - \textcolor{b l u e}{\left({x}^{2} - 4\right) \left(- x + 2\right)}$
into standard form, we must first expand the expression on the right side:

$y = \textcolor{red}{\left(4 {x}^{2} - 12 x\right)} - \textcolor{b l u e}{\left({x}^{3} + 2 {x}^{2} + 4 x - 8\right)}$

$\textcolor{w h i t e}{\text{XX}} = \textcolor{b l u e}{- {x}^{3}} + \textcolor{red}{4 {x}^{2}} - \textcolor{b l u e}{2 {x}^{2}} \textcolor{red}{- 12 x} - \textcolor{b l u e}{4 x} \textcolor{b l u e}{+ 8}$

$\textcolor{w h i t e}{\text{XX}} = - {x}^{3} + 2 {x}^{2} - 16 x + 8$
(which is in standard form)