Question : If $a+b=3$, then the value of $a^{3}+b^{3}+9ab-27$ is:
Option 1: 24
Option 2: 25
Option 3: 0
Option 4: 27
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Correct Answer: 0
Solution : Given: $a+b=3$ Cubing both sides, we get $(a+b)^3=3^3$ ⇒ $a^3+b^3+3ab(a+b)=27$ Putting, $(a+b)=3$ ⇒ $a^3+b^3+3ab×3=27$ ⇒ $a^3+b^3+9ab=27$ Thus, $a^3+b^3+9ab–27=0$ Hence, the correct answer is 0.
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