If \(7^2\) is represented as \((5+2)^2\), the whole area is formed by the sum of how many regions?

Correct answer: 4

The correct answer is C, 4. Write \(7^2\) as \((5+2)^2\). A square whose side is split into 5 and 2 is divided in both directions. This creates four regions: a square of area \(5^2\), one rectangle of area \(5\times2\), a second rectangle of area \(5\times2\), and a square of area \(2^2\). Thus the total area is \(5^2+5\cdot2+5\cdot2+2^2=25+10+10+4=49=7^2\). A and B do not count all four pieces. D invents an extra region; the two cross-regions are already exactly two rectangles. Memory cue: every square-of-a-sum area model has one first square, two cross-rectangles, and one second square—four regions.