What is the value of \(17^3-9^3-8^3\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3672
The numbers \(17\), \(-9\) and \(-8\) add up to zero, and when three numbers add up to zero, the sum of their cubes equals three times their product: \(a+b+c=0\Rightarrow a^3+b^3+c^3=3abc\).
\(a=17\), \(b=-9\), \(c=-8\): \(a+b+c=17-9-8=0\)
\(17^3+(-9)^3+(-8)^3=3\times17\times(-9)\times(-8)\)
\(17^3-9^3-8^3=3\times17\times72=3672\)