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

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Answer 1 · 2015-04-09T12:56:55

We can write this expression as $x^3-(2y)^3$

The formula for factorizing the Difference of two Cubes is:
$a^3−b^3=(a−b)(a^2+ab+b^2)$

In $x^3-(2y)^3$ ,
$a=x$
$b=2y$

$x^3-(2y)^3$
$= (x-2y)*(x^2+(x*2y)+(2y)^2)$
$= color(green)( (x-2y)*(x^2+2xy+4y^2)$

As we cannot factorize any of the factors further, we can say that we have factorised $x^3-8y^3$ completely.

How do you factor x^3-8y^3x^3-8y^3?