# What is the standard form of  y= (-2x+5)^3-(2x+2)^2?

Nov 16, 2017

This is a form of:
$y = a {x}^{3} + b {x}^{2} + c x + d$

#### Explanation:

$y = {\left(- 2 x + 5\right)}^{3} - {\left(2 x + 2\right)}^{2}$
$\implies y = \left(- 2 x + 5\right) \cdot \left(- 2 x + 5\right) \cdot \left(- 2 x + 5\right) - \left(2 x + 2\right) \cdot \left(2 x + 2\right)$
$\implies y = \left(4 {x}^{2} - 20 x + 25\right) \cdot \left(- 2 x + 5\right) - \left(4 {x}^{2} + 8 x + 4\right)$

$\left(4 {x}^{2} - 20 x + 25\right) \cdot \left(- 2 x + 5\right) = - 8 {x}^{3} + 20 {x}^{2} + 40 {x}^{2} - 100 x - 50 x + 125$
$= - 8 {x}^{3} + 60 {x}^{2} - 150 x + 125$

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$- \left(4 {x}^{2} + 8 x + 4\right) = - 4 {x}^{2} - 8 x - 4$

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$y = {\left(- 2 x + 5\right)}^{3} - {\left(2 x + 2\right)}^{2} = \ldots = - 8 {x}^{3} + 60 {x}^{2} - 150 x + 125 - 4 {x}^{2} - 8 x - 4$
$\implies y = - 8 {x}^{3} + 56 {x}^{2} - 158 x + 121$

This is a form of:
$y = a {x}^{3} + b {x}^{2} + c x + d$
for
$a = - 8 , b = 56 , c = - 158 , d = 121$