Question : If $m+n=-2$, then the value of $m^{3}+n^{3}-6mn$ is:
Option 1: 8
Option 2: 4
Option 3: –8
Option 4: –4
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Correct Answer: –8
Solution : Given: $m+n=-2$ and $ab=24$ We know that $(a+b)^3=a^3+b^3+3ab(a+b)$ Now, $m+n=-2$ Cubing both sides. ⇒ $-2^3=m^3+n^3+3(mn)(-2)$ ⇒ $m^3+n^3-6mn=-8$ Hence, the correct answer is –8.
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