# What is the standard form of  y= (-4x+4)^3-(5x+12)^2?

Mar 11, 2018

$y = - 64 {x}^{3} + 167 {x}^{2} - 312 x - 80$

#### Explanation:

The standard form of a cubic function is :

$y = a {x}^{3} + b {x}^{2} + c x + d$

Therefore after expanding

${\left(- 4 x - 4\right)}^{3}$

= $- 64 {x}^{3} + 192 {x}^{2} - 192 x + 64$

and

${\left(5 x + 12\right)}^{2}$

= $25 {x}^{2} + 120 x + 144$

We can join the 2 expressions

$y = \left(- 64 {x}^{3} + 192 {x}^{2} - 192 x + 64\right) - \left(25 {x}^{2} + 120 x + 144\right)$

$y = - 64 {x}^{3} + 167 {x}^{2} - 312 x - 80$