How do to you factor 8x^3 + 125y^6?

Apr 14, 2015

We can modify the expression to use the Sum of Cubes formula to factorise it.

$8 {x}^{3} + 125 {y}^{6} = {\left(2 x\right)}^{3} + {\left(5 {y}^{2}\right)}^{3}$

The formula says :color(blue)(a^3 + b^3 = (a + b)(a^2-ab+b^2)

Here, $a$ is $2 x$ and $b$ is $5 {y}^{2}$

${\left(2 x\right)}^{3} + {\left(5 {y}^{2}\right)}^{3} = \left(2 x + 5 {y}^{2}\right) \left\{{\left(2 x\right)}^{2} - \left(2 x\right) \left(5 {y}^{2}\right) + {\left(5 {y}^{2}\right)}^{2}\right\}$

 color(green)(= (2x + 5y^2){4x^2 - 10xy^2 + 25y^4}

As none of the factors can be factorised further, this becomes the Factorised form of $8 {x}^{3} + 125 {y}^{6}$