Which expansion is correct for the visual model of a square with side \((2p-7)\)?

Correct answer: \(4p^2-28p+49\)

Answer: C, \(4p^2-28p+49\). The square’s area is \((2p-7)^2\). Apply \((u-v)^2=u^2-2uv+v^2\), where \(u=2p\) and \(v=7\). The first square is \((2p)^2=4p^2\). Two strips are removed, each with area \((2p)(7)=14p\), so together they contribute \(-28p\). The small corner square has area \(7^2=49\). Therefore the result is \(4p^2-28p+49\), so C is correct. A has only one strip’s contribution and therefore uses \(-14p\). B has the wrong positive sign; subtraction creates a negative middle term. D incorrectly treats \((2p)^2\) as \(2p^2\) instead of \(4p^2\). Memory cue: in \((u-v)^2\), the first and last terms are positive, but the middle term is negative and doubled.