What are the factors of $x^{3} y^{6} - 64$ $x^3y^6 – 64$ ?

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Answer 1 · 2014-10-29T00:58:45

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

$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ $a^3 -b^3 = (a - b)(a^2 +ab +b^2)$

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

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

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

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What are the factors of x3y6–64x^3y^6 – 64?