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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:
$(a-3 b)^3+(3 b-c)^3+(c-a)^3$
 
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Answer

$(a-3 b)^3+(3 b-c)^3+(c-a)^3$
$\text { Let }(a-3 b)=x,(3 b-c)=y,(c-a)=z$
$x+y+z=a-3 b+3 b-c+c-a=0$
$\because x+y+z=0$
$\therefore x^3+y^3+z^3=3 x y z$
$\therefore(a-3 b)^3+(3 b-c)^3+(c-a)^3$
$=3(a-3 b)(3 b-c)(c-a)$

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