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Factorisation of Algebraic Expressions Using Identities

Evaluate : 2x...

Question

Evaluate : $(2 x - 5 y) (3 x + 7 y) (8 x - 9 y)$ .

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Solution

$(2 x - 5 y) (3 x + 7 y) (8 x - 9 y)$
$= [2 x (3 x + 7 y) - 5 y ((3 x + 7 y))] (8 x - 9 y)$
$= [6 x^{2} + 14 x y - 15 x y - 35 y^{2}] (8 x - 9 y)$
$= [6 x^{2} - x y - 35 y^{2}] (8 x - 9 y)$
$= 6 x^{2} (8 x - 9 y) - x y (8 x - 9 y) - 35 y^{2} (8 x - 9 y)$
$= 48 x^{3} - 54 x^{2} y - 8 x^{2} y + 9 x y^{2} - 280 x y^{2} + 315 y^{3}$
$= 48 x^{3} - 62 x^{2} y - 271 x y^{2} + 315 y^{3}$

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