# How do you factor 8x^3 - 36x^2 + 54x - 27?

Sep 28, 2015

Notice that $8 {x}^{3} = {\left(2 x\right)}^{3}$ and $- 27 = {\left(- 3\right)}^{3}$, so is the answer ${\left(2 x - 3\right)}^{3}$ ?

Multiply out ${\left(2 x - 3\right)}^{3}$ and find that it is.

$8 {x}^{3} - 36 {x}^{2} + 54 x - 27 = {\left(2 x - 3\right)}^{3}$

#### Explanation:

In general, ${\left(a + b\right)}^{3} = {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$

Putting $a = 2 x$ and $b = - 3$ we find:

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

$= 8 {x}^{3} - 36 {x}^{2} + 54 x - 27$