MCQ
If $\mathrm{a}-\mathrm{b}=-8$ and $\mathrm{ab}=-12$, then $\mathrm{a}^3-\mathrm{b}^3=$
- A$-244$
- B$-240$
- ✓$-224$
- D$-260$
✓
Answer
Correct option: C.
$-224$
$a-b=-8$
$(a-b)^2=64$
$a^2+b^2-2 a b=64$
$a^2+b^2-2 a b+3 a b=64+3 a b$
$a^2+b^2+a b=64+3(-12)$
$a^2+b^2+a b=64-36$
$a^2+b^2+a b=28$
Now
$a^3-b^3=(a-b)\left(a^2+b^2+a b\right)$
$=(-8)(28)$
$=-224$
Hence, correct option is $(c)$.
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