How do you factor $x^{3} - 8$ $x^3 -8$ ?

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Answer 1 · 2014-10-29T01:09:55

$x^{3} - 8$ $x^3 - 8$ 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

$x^{3}$ $x^3$ factors to x
$8$ $8$ factors to 2

$x^{3} - 8 = (x - 2) (x^{2} + 4 x + 4)$ $x^3 - 8 = (x - 2)(x^2 + 4x + 4)$

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How do you factor x3−8x^3 -8?