Which expression is the square of the binomial \(3p-4q\)?

Correct answer: \(9p^2-24pq+16q^2\)

The correct answer is A. Use the identity \((a-b)^2=a^2-2ab+b^2\). Here \(a=3p\) and \(b=4q\). Squaring the first term gives \(9p^2\), the cross term is \(-2(3p)(4q)=-24pq\), and the square of the second term is \(16q^2\). Thus \((3p-4q)^2=9p^2-24pq+16q^2\). Option B has the wrong final coefficient: the square of \(4q\) is \(16q^2\), not \(12q^2\). Option C has an incorrect middle coefficient; it should be \(-24pq\), not \(-18pq\). Option D has both the wrong sign and wrong middle coefficient. The minus sign inside the binomial creates a negative cross term, but the last term remains positive because a square is nonnegative in the algebraic identity. Memory cue: square first, double product with the same sign as the bracket’s cross term, then square the second term.