How do you find the product of (x-y)(x^2+xy+y^2)?

Oct 19, 2016

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

Explanation:

We must ensure that each term in the second bracket is multiplied by each term in the first bracket.
This can be achieved as follows.

$\textcolor{red}{x} \left(\textcolor{b l u e}{{x}^{2} + x y + {y}^{2}}\right) \textcolor{red}{- y} \left(\textcolor{b l u e}{{x}^{2} + x y + {y}^{2}}\right)$

now distribute the brackets.

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

collect like terms.

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

$= {x}^{3} - {y}^{3} \leftarrow \text{ a difference of cubes}$