MCQ
If $a - b = -8$ and $ab = -12,$ then $a^3 - b^3 =$
- A$-260$
- B$-244$
- ✓$-224$
- D$-240$
✓
Answer
Correct option: C.
$-224$
$\text { Using, }(a-b)^3=a^3-b^3-3 a b(a-b)$
$\Rightarrow a^3-b^3=(a-b)^3+3 a b(a-b)$
$\Rightarrow a^3-b^3=(-8)^3+3(-12)(-8)$
$\Rightarrow a^3-b^3=-512+288=-224$
$\Rightarrow a^3-b^3=(a-b)^3+3 a b(a-b)$
$\Rightarrow a^3-b^3=(-8)^3+3(-12)(-8)$
$\Rightarrow a^3-b^3=-512+288=-224$
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