Question : If $a-b=2$ and $ab=24$, then what is the value of $a^3-b^3$?
Option 1: 280
Option 2: 124
Option 3: 140
Option 4: 152
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Correct Answer: 152
Solution :
Given: $a-b=2$ and $ab=24$
We know that $(a-b)^3=a^3-b^3-3ab(a-b)$
⇒ $2^3=a^3-b^3-3(24)(2)$
⇒ $a^3-b^3=8+3\times 24\times 2$
⇒ $a^3-b^3=152$
Hence, the correct answer is 152.
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