What should replace the question mark?
\(\displaystyle\frac{854\times854\times854-276\times276\times276}{854\times854+854\times276+276\times276}=?\)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 578
The expression has the form of the identity \(a^3-b^3=(a-b)(a^2+ab+b^2)\), with \(a=854\) and \(b=276\). The numerator is \(a^3-b^3\) and the denominator is \(a^2+ab+b^2\), so the denominator cancels and no large multiplication is needed.
After the cancelling, only the first factor is left: \(\displaystyle\frac{a^3-b^3}{a^2+ab+b^2}=a-b\)
So the value is the difference of the two numbers: \(854-276=578\)