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

Mar 29, 2018

$y = - 28 {x}^{3} + 30 {x}^{2} - 12 x + 2$

#### Explanation:

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

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

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

$y = 1 - 3 x + 3 {x}^{2} - {x}^{3} + 1 - 9 x + 27 {x}^{2} - 27 {x}^{3}$

$y = - {x}^{3} - 27 {x}^{3} + 3 {x}^{2} + 27 {x}^{2} - 9 x - 3 x + 1 + 1$

$y = - 28 {x}^{3} + 30 {x}^{2} - 12 x + 2$