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Factorisation of Polynomials — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSFactorisation of Polynomials2 Marks
Question
Factorise:$3a^7b - 81a^4b^4$
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Answer

$3a^7b - 81a^4b^4$
$= 3a^4b(a^3 - 27b^3)$
$= 3a^4b[(a)^3 - (3b)^3]$
$= 3a^4b(a - 3b)[(a)^2 + a \times 3b + (3b)^2] Since a^3 - b^3 = (a - b)(a^2 + a \times b + b^2)$
$= 3a^4b(a - 3b)(a^2 + 3ab + 9b^2)$

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