# What is the standard form of  y= (2x+4)(-x+5)(-x+1)?

May 21, 2017

$y = - 2 {x}^{3} - 8 {x}^{2} - 14 x + 1$

#### Explanation:

$y = \left(- 2 {x}^{2} + 10 x - 4 x + 20\right) \left(- x + 1\right)$
$y = \left(- 2 {x}^{2} + 6 x + 20\right) \left(- x + 1\right)$
$y = - 2 {x}^{3} - 2 {x}^{2} - 6 {x}^{2} + 6 x - 20 x + 1$
$y = - 2 {x}^{3} - 8 {x}^{2} - 14 x + 1$

Always factor the harder one first, otherwise, factor left to right.

May 25, 2017

color(blue)(y=2x^3-8x^2-14x+20

#### Explanation:

$y = \left(2 x + 4\right) \left(- x + 5\right) \left(- x + 1\right)$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$2 x + 4$
$\textcolor{w h i t e}{a a a a a a a a a a}$$\times \underline{- x + 5}$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$- 2 {x}^{2} - 4 x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$10 x + 20$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\overline{- 2 {x}^{2} + 6 x + 20}$
$\textcolor{w h i t e}{a a a a a a a a}$$\times - x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$$\overline{2 {x}^{3} - 6 {x}^{2} - 20 x}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a}$$- 2 {x}^{2} + 6 x + 20$
$\textcolor{w h i t e}{a a a a a a a a}$color(blue)(y=overline(2x^3-8x^2-14x+20)