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Factorisation of Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsFactorisation of Polynomials2 Marks
Question
Factorise:
$(a x+b y)^2+(b x-a y)^2$
 
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Answer

$(a x+b y)^2+(b x-a y)^2$
$=a^2 x^2+b^2 y^2+2 a b x y+b^2 x^2+a^2 y^2-2 a b x y$
$=a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2$
$=a^2 x^2+b^2 x^2+b^2 y^2+a^2 y^2$
$=x^2\left(a^2+b^2\right)+y^2\left(a^2+b^2\right)$
$=\left(a^2+b^2\right)\left(x^2+y^2\right)$

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