Factorize the following expressions: 8 x^3-125 y^3+180 x y+216 - Vidyadip

Question

Factorize the following expressions:
$8 x^3-125 y^3+180 x y+216$

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Answer

$8 x^3-125 y^3+180 x y+216$
$\text { or, } 8 x^3-125 y^3+216+180 x y$
$=(2 x)^3+(-5 y)^3+6^3-3 x(2 x)(-5 y)(6)$
$=(2 x+(-5 y)+6)\left((2 x)^2+(-5 y)^2+6^2-2 x(-5 y)-(-5 y) 6-6(2 x)\right)$
$=(2 x-5 y+6)\left(4 x^2+25 y^2+36+10 x y+30 y-12 x\right)$
$\therefore 8 x^3-125 y^3+180 x y+216$
$=(2 x-5 y+6)\left(4 x^2+25 y^2+36+10 x y+30 y-12 x\right)$

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