The value of \(\frac{(8.9)^2-(2.1)^2}{8.9-2.1}\)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 11.0
The numerator is a difference of two squares, and \(a^{2}-b^{2}=(a+b)(a-b)\). The factor \(a-b\) then cancels with the denominator, so no squaring is needed.
\(\displaystyle \frac{(8.9)^{2}-(2.1)^{2}}{8.9-2.1}=\frac{(8.9+2.1)(8.9-2.1)}{8.9-2.1}\)
\(=8.9+2.1=11.0\)