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

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

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Answer 1 · 2017-02-13T04:46:34

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

Explanation:

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

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

= $(5 x + 2 g) ({(5 x)}^{2} - (5 x) \times (2 g) + {(2 g)}^{2})$ $(5x+2g)((5x)^2-(5x)xx(2g)+(2g)^2)$

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

For a proof of the identity see below.

$x^{3} + y^{3}$ $x^3+y^3$

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

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

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

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

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Explanation:

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