What is the value of \(\displaystyle\frac{387^{2}-213^{2}}{174}\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 600
A difference of two squares splits as \(a^{2}-b^{2}=(a-b)(a+b)\). Here \(a-b\) is the same as the denominator, so the two cancel without squaring anything.
\(a=387,\ b=213\)
\(a-b=387-213=174\) and \(a+b=387+213=600\)
\(\displaystyle\frac{174\times600}{174}=600\)