Discussion
Evaluate : \(\dfrac{(2.39)^2 - (1.61)^2}{2.39 - 1.61}\)
Answer: B
Again the numerator is a difference of two squares, so the whole expression collapses to the sum of the two numbers.
\[ \frac{a^{2}-b^{2}}{a-b} = \frac{(a+b)(a-b)}{a-b} = a+b \]
\[ \frac{(2.39)^{2}-(1.61)^{2}}{2.39-1.61} = 2.39 + 1.61 = 4 \]
The awkward decimals are deliberate: they punish anyone who squares first (\( 5.7121 - 2.5921 = 3.12 \), then \( 3.12 \div 0.78 = 4 \)) and reward spotting the identity.
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