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Algebraic Expressions, Identities and Factorisation — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSAlgebraic Expressions, Identities and Factorisation2 Marks
Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$ (x+y)^4-(x-y)^4 $
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Answer

$ (x+y)^4-(x-y)^4 $
$ =\left[(x+y)^2\right]^2-\left[(x-y)^2\right]^2 $
$ =\left[(x+y)^2+(x-y)^2\right]\left[(x+y)^2-(x-y)^2\right] $
$ =\left(x^2+y^2+2 x y+x^2+y^2-2 x y\right)(x+y+x-y)(x+y-x+y) $
$ =\left(2 x^2+2 y^2\right)(2 x)(2 y) $
$ =2\left(x^2+y^2\right)(2 x)(2 y) $
$ =8 x y\left(x^2+y^2\right) $

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