What are the factors of x^3y^6 – 64?

Oct 29, 2014

${x}^{3} {y}^{6} - 64$ is the difference of two cubes and can be factored in the following pattern.

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

${a}^{3}$ factors to a
${b}^{3}$ factors to b

The pattern of the signs follows the acronym SOAP
S = same sign as the cubes
O = opposite sins of the cubes
AP = always positive

${x}^{3} {y}^{3}$ factors to xy
$64$ factors to 4

${x}^{3} {y}^{3} - 64 = \left(x y - 4\right) \left({x}^{2} {y}^{2} + 4 x y + 16\right)$