Question

Simplify the following expression:

\(\frac{108\times108\times108-92\times92\times92}{108\times108+92\times92+108\times92}\)

1. 200
2. 16
3. 1
4. -1

Answer 1

Correct Answer - Option 2 : 16

Given:

\(\frac{108\times108\times108-92\times92\times92}{108\times108+92\times92+108\times92}\)

Formula used:

(a)³ – (b)³ = (a – b)(a² + b² + ab)

Calculation:

\(\frac{108\times108\times108-92\times92\times92}{108\times108+92\times92+108\times92}\)

⇒ \(\frac{(108)^3\;-\;(92)^3}{(108)^2\;+\;(92)^2\;+\;108\;\times\;92}\)

⇒ \(\frac{(108\;-\;92)[(108)^2\;+\;(92)^2\;+\;108\;\times\;92]}{(108)^2\;+\;(92)^2\;+\;108\;\times\;92}\)

⇒ 108 – 92

⇒ 16

∴ Required answer is 16