# What is the standard form of  y= (-x-9)^3-(2x-1)^2?

Jul 8, 2017

color(magenta)(y=-x^3-31x^2-239x-730

#### Explanation:

$y = {\left(- x - 9\right)}^{3} - {\left(2 x - 1\right)}^{2}$

$y = - {x}^{3} - 27 {x}^{2} - 243 x - 729 - \left(4 {x}^{2} - 4 x + 1\right)$

color(magenta)(y=-x^3-31x^2-239x-730

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- x - 9$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{- x - 9}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$${x}^{2} + 9 x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a}$$9 x + 81$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$$\overline{{x}^{2} + 18 x + 81}$
$\textcolor{w h i t e}{a a a a a a a a a}$$\times - x - 9$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$\overline{- {x}^{3} - 18 {x}^{2} - 81 x}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$- 9 {x}^{2} - 162 x - 729$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\overline{- {x}^{3} - 27 {x}^{2} - 243 x - 729}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$$2 x - 1$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{2 x - 1}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$4 {x}^{2} - 2 x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a}$$- 2 x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{4 {x}^{2} - 4 x + 1}$