Which is the factorised form of (64a^2+80ab+25b^2)?

Correct answer: \((8a+5b)^2\)

Direct answer: A, \((8a+5b)^2\). Use the identity \((P+Q)^2=P^2+2PQ+Q^2\). Here choose \(P=8a\) and \(Q=5b\). Then \(P^2=64a^2\), \(Q^2=25b^2\), and \(2PQ=2(8a)(5b)=80ab\). These are exactly the three terms in the given expression, so it equals \((8a+5b)^2\). Option B uses a minus sign; its middle term would be \(-80ab\), not \(+80ab\). Option C squares the whole terms incorrectly and would have degree-four terms such as \(a^2b^2\) after expansion. Option D expands to \(64a^2+208ab+25b^2\), so its middle coefficient is wrong. A useful check is that the square roots of the first and last terms are \(8a\) and \(5b\); the middle term must be twice their product, with the same sign as the bracket.