# How do you expand (x-y)^3?

Apr 10, 2018

=${x}^{3} - 3 {x}^{2} y + 3 x {y}^{2} - {y}^{3}$

#### Explanation:

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

=${x}^{2} - 2 x y + {y}^{2}$

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

=${x}^{3} - {x}^{2} y - 2 {x}^{2} y + 2 x {y}^{2} + x {y}^{2} - {y}^{3}$

=${x}^{3} - 3 {x}^{2} y + 3 x {y}^{2} - {y}^{3}$

May 8, 2018

${x}^{3} - {y}^{3} - 3 {x}^{2} y + 3 x {y}^{2}$

#### Explanation:

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

Expand the first two brackets:

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

$\Rightarrow {x}^{2} + {y}^{2} - 2 x y$

Multiply the result by the last two brackets:

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

$\Rightarrow {x}^{3} - {y}^{3} - 3 {x}^{2} y + 3 x {y}^{2}$

Always expand each term in the bracket by all the other terms in the other brackets, but never multiply two or more terms in the same bracket.