Choose the correct factorisation of \(25r^2-30r+9\).

Correct answer: \((5r-3)^2\)

The direct answer is C: \((5r-3)^2\). The first term is \(25r^2=(5r)^2\), and the last term is \(9=3^2\). For the identity \((m-n)^2=m^2-2mn+n^2\), the middle term should be \(-2(5r)(3)=-30r\), exactly as given. Hence \(25r^2-30r+9=(5r-3)^2\). A is incorrect because \((5r+3)^2\) gives \(+30r\), not \(-30r\). B has the wrong leading term and does not produce the required polynomial. D expands to \(25r^2-50r+9\), so its middle coefficient is wrong. Always verify a factorisation by expanding it, especially when signs are involved. The sign of the middle term tells us whether the binomial uses a plus or minus sign.