# How do you multiply and simplify the following expression completely (x-2y)^3?

Mar 24, 2015

The rule is:

${\left(a - b\right)}^{3} = {a}^{3} - 3 {a}^{2} b + 3 a {b}^{2} - {b}^{3}$.

So:

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

$= {x}^{3} - 6 {x}^{2} y + 12 x {y}^{2} - 8 {y}^{3}$.