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