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

May 29, 2018

color(purple)(=>-64x^3 + 143x^2 - 132x - 117 is the standard form with polynomial degree 3 and number of terms 4.

#### Explanation:

${\left(a - b\right)}^{3} = {a}^{3} - {b}^{3} - 3 {a}^{2} b + 3 a {b}^{2}$ identity

${\left(- 4 x + 3\right)}^{3} - {\left(x + 12\right)}^{2}$

=> (27 - 64x^3 - 108x + 144x^2 - x^2 - 24x - 144

$\implies - 64 {x}^{3} + 144 {x}^{2} - x {-}^{2} - 108 x - 24 x + 27 - 144$

color(purple)(=>-64x^3 + 143x^2 - 132x - 117 is the standard form with polynomial degree 3 and number of terms 4.