How do you factor $125x^3+8g^3$ ?

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Answer 1 · 2017-02-13T04:46:34

$125x^3+8g^3=(5x+2g)(25x^2-10xg+4g^2)$

As $125x^3+8g^3=(5x)^3+(2g)^3$ , it can be factorized using identity $x^3+y^3=(x+y)(x^2-xy+y^2)$

and $125x^3+8g^3=(5x)^3+(2g)^3$

= $(5x+2g)((5x)^2-(5x)xx(2g)+(2g)^2)$

= $(5x+2g)(25x^2-10xg+4g^2)$

For a proof of the identity see below.

$x^3+y^3$

= $x^3+x^2y-x^2y-xy^2+xy^2+y^3$

= $x^2(x+y)-xy(x+y)+y^2(x+y)$

= $(x+y)(x^2-xy+y^2)$

How do you factor 125x^3+8g^3125x^3+8g^3?