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

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Answer 1 · 2015-05-21T22:20:53

$125 x^{3} + 8 y^{3}$ $125x^3+8y^3$

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

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

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

using the standard factorisation:

$(a^{3} + b^{3}) = (a + b) (a^{2} - a b + b^{2})$ $(a^3+b^3) = (a+b)(a^2-ab+b^2)$

How do you factor 125x^3 + 8y^3125x3+8y3125x^3 + 8y^3?