Factorization Of Algebraic Expressions — Maths STD 9 — Question
CBSE BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions1 Mark
MCQ
If $a^3-(b-a)^3-b^3=k(a-b)$, then $k=$
A
ab
B
3 ab
C
$-3 a b$
D
3
✓
Answer
B. 3 ab We observe that $a+(b-a)+(-b)=0$.\[\begin{array}{ll}\therefore & a^3+(b-a)^3+(-b)^3=3 a(b-a)(-b) \\\Rightarrow & a^3-(b-a)^3-b^3=3 a b(a-b) \Rightarrow k(a-b)=3 a b(a-b) \Rightarrow k=3 a b\end{array}\]
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