# How do you simplify (-3x + 1)^3?

Apr 23, 2017

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

#### Explanation:

Given -

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

It is like ${\left(a + b\right)}^{3}$
${\left(a + b\right)}^{3} = {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$

In the given expression -

$a = - 3 {x}^{2}$
$b = 1$

Use the standard binomial expansion to simplify the given expression.

${\left(- 3 x\right)}^{3} + \left[3. {\left(- 3 x\right)}^{2.1}\right] + \left[3. \left(- 3 x\right) {.1}^{2}\right] + {1}^{3}$

On simplifying you get

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