What is the value of \(\displaystyle\frac{(7.5)^{3}-(2.5)^{3}}{(7.5)^{2}+7.5\times2.5+(2.5)^{2}}\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5
Use the identity \(a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})\). The denominator is exactly \(a^{2}+ab+b^{2}\), so it cancels.
Here \(a=7.5\) and \(b=2.5\)
\(\displaystyle\frac{(a-b)(a^{2}+ab+b^{2})}{a^{2}+ab+b^{2}}=a-b\)
\(a-b=7.5-2.5=5\)