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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