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Polynomials — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSPolynomials1 Mark
Question
$(x + y)^3 - (x - y)^3$ can be factorized as:
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Answer

Put $a = x + y$ and $b = x - y,$ then
$(x + y)^3 - (x - y)^3 = a^3 - b^3$
$= (a − b) (a^2 + b^2 + ab)$
$= (x + y - x + y) [(x + y)^2 + (x - y)^2 + (x - y) (x+y)]$
$=2y[2(x^2 + y^2) + (x^2 - y^2)]$
$=2y[3x^2 + y^2]$

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