\( 25m^2-70mn+49n^2 \) is the square of what?

Correct answer: \((5m-7n)^2\)

The first term is \(25m^2=(5m)^2\), and the last term is \(49n^2=(7n)^2\). Using \((a-b)^2=a^2-2ab+b^2\), with \(a=5m\) and \(b=7n\), the middle term becomes \(-2(5m)(7n)=-70mn\). Hence the expression is \((5m-7n)^2\). In contrast, \((5m+7n)^2\) would have the positive middle term \(+70mn\). Exam tip: while identifying a perfect square, always check the sign of the middle term and verify \(2ab\).