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Playing With Numbers — MATHS STD 6 — Question

Gujarat BoardEnglish MediumSTD 6MATHSPlaying With Numbers1 Mark
MCQ
Factors of $(a+b)^3 - (a-b)^3$ are:
  • A
    $2ab(3a^2+b^2)$
  • B
    $ab(3a^2+b^2)$
  • ✓
    $2b(3a^2+b^2)$
  • D
    $3a^2+b^2$
✓

Answer

Correct option: C.
$2b(3a^2+b^2)$
$(a + b)^3 - (a - b)^3$
$\Rightarrow a^3 + 3a^2b + 3ab^2 + b^3 - (a^3 - 3a^2b + 3ab^2 - b^3)$
$\Rightarrow a^3 + 3a^2b + 3ab^2 + b^3 - a^3 - 3a^2b + 3ab^2 - b^3$
$\Rightarrow 6a^2b + 2b^3$
$\Rightarrow 2b (3a^2 + b^2)$

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