Factorize: 60x^3 y + 115x^2 y^2 − 120xy^3


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Question Number 41710 by Tawa1 last updated on 11/Aug/18

$Factorize : {60 x}^{3} y + {115 x}^{2} y^{2} - {120 xy}^{3}$
	Answered by alex041103 last updated on 11/Aug/18

	${60 x}^{3} y + {115 x}^{2} y^{2} - 120 x y^{3} =$ $= 5 x y (12 x^{2} + 23 x y - 24 y^{2})$ $T h e n {l e t}^{'} s f i n d x_{1, 2} f o r$ $(12) x^{2} + (23 y) x + (- 24 y^{2}) = 0$ $\Rightarrow x_{1, 2} = \frac{- 23 y \pm \sqrt{529 y^{2} + 1152 y^{2}}}{24} =$ $= \frac{\pm \sqrt{1681} - 23}{24} y = \frac{- 23 \pm 41}{24} y = - \frac{8}{3} y o r \frac{3}{4} y$ $\Rightarrow (12 x^{2} + 23 x y - 24 y^{2}) = 12 (x + \frac{8}{3} y) (x - \frac{3}{4} y)$ $= (3 x + 8 y) (4 x - 3 y)$ $\Rightarrow {60 x}^{3} y + {115 x}^{2} y^{2} - 120 x y^{3} =$ $= 5 x y (3 x + 8 y) (4 x - 3 y)$
	Commented by Tawa1 last updated on 11/Aug/18

	$I really appreciate sir . God bless you sir$
	Answered by ajfour last updated on 11/Aug/18

	$= 5 x y (12 x^{2} + 23 x y - 24 y^{2})$ $= 5 x y (12 x^{2} + 32 x y - 9 x y - 24 y^{2})$ $= 5 x y [4 x (3 x + 8 y) - 3 y (3 x + 8 y)]$ $= 5 x y (3 x + 8 y) (4 x - 3 y) .$
	Commented by Tawa1 last updated on 11/Aug/18

	$God bless you sir$
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