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Factorization Of Algebraic Expressions — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
Factorize the following expressions:
$1-27 a^3$
 
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Answer

$1-27 a^3$
$=(1)^3-(3 a)^3$
$=(1-3 a)\left(1^2+1 \times 3 a+(3 a)^2\right)$
$\therefore\left[a^3-b^3=(a-b)\left(a^2+a b+b^2\right)\right]$
$=(1-3 a)\left(1^2+3 a+9 a^2\right)$
$\therefore 1-27 a^3=(1-3 a)\left(1^2+3 a+9 a^2\right)$

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