Question : If $a-b=8$ and $4ab=84$, then what is the value of $3a^3-3b^3$?
Option 1: 1016
Option 2: 2032
Option 3: 1018
Option 4: 3048
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Correct Answer: 3048
Solution : Given: $a-b=8$ and $4ab=84$ ⇒ $ab=21$ Now, $a-b=8$ Cubing both sides we get, ⇒ $(a-b)^3=8^3$ ⇒ $a^3-b^3-3ab(a-b)=512$ Putting the values, we get: ⇒ $a^3-b^3-3\times 21\times8=512$ ⇒ $a^3-b^3=512+504$ ⇒ $a^3-b^3=1016$ $\therefore 3a^3-3b^3 =3\times1016=3048$ Hence, the correct answer is 3048.
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