A rectangle has length \(a+b\) and breadth \(a-b\). What is its area?

Correct answer: \(a^2-b^2\)

The direct answer is A: \(a^2-b^2\). The area of a rectangle is length times breadth, so write \((a+b)(a-b)\). Multiply the terms: \(a(a-b)+b(a-b)=a^2-ab+ab-b^2\). The middle terms \(-ab\) and \(+ab\) cancel, leaving \(a^2-b^2\). This is the difference-of-squares identity \((a+b)(a-b)=a^2-b^2\). B is the expansion of \((a+b)^2\), which would be the area of a square whose two sides are both \(a+b\). C is the expansion of \((a-b)^2\), which would require both dimensions to be \(a-b\). D is related to adding lengths or perimeter-like expressions, not multiplying the rectangle's dimensions. Memory cue: a sum times the matching difference cancels the middle terms, so only the two squares remain.