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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:
$(3 x-2 y)^3+(2 y-4 z)^3+(4 z-3 x)^3$
 
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Answer

$(3 x-2 y)^3+(2 y-4 z)^3+(4 z-3 x)^3$
$\text { Let }(3 x-2 y)=a,(2 y-4 z)=b,(4 z-3 x)=c$
$\therefore a+b+c=3 x-2 y+2 y-4 z+4 z-3 x=0$
$\because a+b+c=0$
$\therefore a^3+b^3+c^3+3 a b c$
$\therefore(3 x-2 y)^3+(2 y-4 z)^3+(4 z-3 x)^3$
$=3(3 x-2 y)(2 y-4 z)(4 z-3 x)$

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