Question

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

Answer 1

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

`8x^3 + 125y^6 = (2x)^3 + (5y^2)^3`

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

Here, `a` is `2x` and `b` is `5y^2`

`(2x)^3 + (5y^2)^3 = (2x + 5y^2){(2x)^2 - (2x)(5y^2) + (5y^2)^2}`

`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 `8x^3 + 125y^6`