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

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Answer 1 · 2015-04-14T05:36:47

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 $8x^3 + 125y^6$

How do to you factor 8x^3 + 125y^68x^3 + 125y^6?