# What is difference of two cubes method for factoring?

${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$
You can verify that the formula is correct by multiplying the right side of the equation. Multiplying $a$ times each term in the secon factor and the $- b$ times each, we get:
$\left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right) = {a}^{3} + {a}^{2} b + a {b}^{2} - {a}^{2} b - a {b}^{2} - {b}^{3}$
As you can see, this simplifies to: ${a}^{3} - {b}^{3}$