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Factorisation of Polynomials — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsFactorisation of Polynomials2 Marks
Question
Factorise:
$8(x+y)^3-27(x-y)^3$
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Answer

$8(x+y)^3-27(x-y)^3$
$\left.=\left[2^3(x+y)^3\right]-\left[3^3(x-y)\right)^3\right]$
$\left.=[2(x+y)-3(x-y)\}[2(x+y)]^2+2(x+y) 3(x-y)+[3(x-y)]^2\right\}$
$=(2 x+2 y-3 x+3 y)\left\{\left[4\left(x^2+y^2+2 x y\right)\right]+6\left(x^2-y^2\right)+\left[9\left(x^2+y^2-2 x y\right]\right\}\right.$
$=(-x+5 y)\left\{4 x^2+4 y^2+8 x y+6 x^2-6 y^2+9 x^2+9 y^2-18 x y\right\}$
$=(-x+5 y)\left(19 x^2+7 y^2-10 x y\right)$

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