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

1 Answer

Jun 28, 2016

$8 x^{3} - y^{3} = (2 x - y) (4 x^{2} + 2 x y + y^{2})$ $8x^3-y^3=color(blue)((2x-y)(4x^2+2xy+y^2)$

Explanation:

In general the difference of cubes can be factored as:
$XXX a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ $color(white)("XXX")a^3-b^3=(a-b)(a^2+ab+b^2)$

For the given example: $a^{3} = 8 x^{3} = {(2 x)}^{3}$ $a^3=8x^3=(2x)^3$ and $b^{3} = y^{3}$ $b^3=y^3$

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