# What is the standard form of  y= (5x-2)^3+(-3x-1)^2?

Dec 26, 2015

$y = 125 {x}^{3} - 141 {x}^{2} + 66 x - 7$

#### Explanation:

To rewrite the equation in standard form, expand the brackets:

$y = {\left(5 x - 2\right)}^{3} + {\left(- 3 x - 1\right)}^{2}$

$y = \left(5 x - 2\right) \left(5 x - 2\right) \left(5 x - 2\right) + \left(- 3 x - 1\right) \left(- 3 x - 1\right)$

Expand the first two $\left(5 x - 2\right)$ brackets.

$y = \left(25 {x}^{2} - 20 x + 4\right) \left(5 x - 2\right) + \left(9 {x}^{2} + 6 x + 1\right)$

Expand the last $\left(5 x - 2\right)$ bracket.

$y = \left(125 {x}^{3} - 100 {x}^{2} + 20 x - 50 {x}^{2} + 40 x - 8\right) + \left(9 {x}^{2} + 6 x + 1\right)$

Group all like-terms together in the first bracket.

$y = \left(125 {x}^{3} - 100 {x}^{2} - 50 {x}^{2} + 20 x + 40 x - 8\right) + \left(9 {x}^{2} + 6 x + 1\right)$

Simplify the like-terms in the first bracket.

$y = \left(125 {x}^{3} - 150 {x}^{2} + 60 x - 8\right) + \left(9 {x}^{2} + 6 x + 1\right)$

Group all like-terms together.

$y = 125 {x}^{3} - 150 {x}^{2} + 9 {x}^{2} + 60 x + 6 x - 8 + 1$

Simplify.

$y = 125 {x}^{3} - 141 {x}^{2} + 66 x - 7$