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

1 Answer
Apr 23, 2015

#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#