# The standard form of y = (x +1)^3 ­- (3x-2)^2?

Jan 6, 2018

Standard form is

$\textcolor{g r e e n}{y = {x}^{3} - 6 {x}^{2} + 15 x - 3}$

#### Explanation:

$y = {\left(x + 1\right)}^{3} - {\left(3 x - 2\right)}^{2}$

Expanding the terms

$y = \left({x}^{3} + 1 + 3 x \left(x + 1\right)\right) - \left(9 {x}^{2} + 4 - 12 x\right)$

Removing the braces,

$y = {x}^{3} + 1 + 3 {x}^{2} + 3 x - 9 {x}^{2} - 4 + 12 x$#

Rearranging the like terms together and the polynomials in descending order to get the standard form

$y = {x}^{3} + 3 {x}^{2} - 9 {x}^{2} + 3 x + 12 x + 1 - 4$

Combining the like terms and simplifying,

$\textcolor{g r e e n}{y = {x}^{2} - 6 {x}^{2} + 15 x - 3}$