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Factorisation of Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsFactorisation of Polynomials2 Marks
Question
Factorise: $(3 a-2 b)^3+(2 b-5 c)^3+(5 c-3 a)^3$
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Answer

Put $(3 a-2 b)=x,(2 b-5 c)=y$ and $(5 c-3 a)=z$.
We have: $x+y+z=3 a-2 b+2 b-5 c+5 c-3 a=0$
Now, $(3 a-2 b)^3$ $+(2 b-5 c)^3+(5 c-3 a)^3=x^3+y^3+z^3=3 x y z\left[\right.$
Here, $x+y+z=0$.
So, $\left.x^3+y^3+z^3\right]=(3 a-2 b)(2 b-5 c)(5 c-3 a)$

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