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

Gujarat BoardEnglish MediumSTD 8MATHSAlgebraic Expressions, Identities and Factorisation2 Marks
Question
Verify the following:
$\left(a^2-b^2\right)\left(a^2+b^2\right)+\left(b^2-c^2\right)\left(b^2+c^2\right)+\left(c^2-a^2\right)+\left(c^2+a^2\right)=0$
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Answer

$\left(a^2-b^2\right)\left(a^2+b^2\right)+\left(b^2-c^2\right)\left(b^2+c^2\right)+\left(c^2-a^2\right)+\left(c^2+a^2\right)=0$
Taking $LHS$
$ =\left(a^2-b^2\right)\left(a^2+b^2\right)+\left(b^2-c^2\right)\left(b^2+c^2\right)+\left(c^2-a^2\right)+\left(c^2+a^2\right) $
$=\left(a^4-b^4+b^4-c^4+c^4-a^4\right)=0$
$= RHS$
Hence verified

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