If a visual model is made for a square of side \(5a-2b\), what will be the expansion?

Correct answer: \(25a^2-20ab+4b^2\)

Answer: A. The area of a square is the square of its side, so we calculate \((5a-2b)^2\). Use \((p-q)^2=p^2-2pq+q^2\), with \(p=5a\) and \(q=2b\). The first square is \((5a)^2=25a^2\), the cross term is \(-2(5a)(2b)=-20ab\), and the last square is \((2b)^2=4b^2\). Therefore the expansion is \(25a^2-20ab+4b^2\). B has the wrong sign because subtraction gives a negative middle term. C forgets the factor 2. D squares neither term correctly. Memory cue: square each end and use twice the product in the middle; the sign follows the sign between the terms.