How do you factor $8x^3 - y^6$ ?

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Answer 1 · 2015-04-23T09:46:38

$8x^3 - y^6 = (2x)^3 - (y^2)^3$

We can use the Identity $color(blue)(a^3 - b^3 = (a - b)(a^2 +ab+b^2)$

We get $(2x - y^2){(2x)^2 +(2x)(y^2)+(y^2)^2}$

$= color(green)((2x - y^2){4x^2 +2xy^2 +y^4}$

As none of the factors above can be factorised further, it is the factorised form of $8x^3 - y^6$

How do you factor 8x^3 - y^68x^3 - y^6?