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

May 2, 2017

:.color(blue)(y=8x^3+20x^2+70x+23

#### Explanation:

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

First simplify ${\left(2 x + 3\right)}^{3}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$2 x + 3$

$\textcolor{w h i t e}{a a a a a a a a a a a}$$\underline{\times 2 x + 3}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$4 {x}^{2} + 6 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 a}$$6 x + 9$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{4 {x}^{2} + 12 x + 9}$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times 2 x + 3$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{8 {x}^{3} + 24 {x}^{2} + 18 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}$$12 {x}^{2} + 36 x + 27$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$overline(color(purple)(8x^3+36x^2+54x+27)

Then simplify color(green)((4x-2)^2

$\textcolor{g r e e n}{= \left(4 x - 2\right) \left(4 x - 2\right)}$

:.color(green)((4x-2)^2=16x^2-16x+4

color(purple)((2x+3)^3=8x^3+36x^2+54x+27

$\therefore y = 8 {x}^{3} + 36 {x}^{2} + 54 x + 27 - \left(16 {x}^{2} - 16 x + 4\right)$

$\therefore \textcolor{\mathmr{and} a n \ge}{y = 8 {x}^{3} + 36 {x}^{2} + 54 x + 27 - 16 {x}^{2} + 16 x - 4}$

:.color(blue)(y=8x^3+20x^2+70x+23