Choose the correct factorised form of (16m^2-40mn+25n^2).

Correct answer: ((4m-5n)^2)

The direct answer is B: \((4m-5n)^2\). Use the identity \((p-q)^2=p^2-2pq+q^2\). Here \(p=4m\) and \(q=5n\). Thus \((4m-5n)^2=(4m)^2-2(4m)(5n)+(5n)^2=16m^2-40mn+25n^2\). Option B matches every coefficient and sign. Option A, \((4m+5n)^2\), would have a positive middle term \(+40mn\), so it is wrong. Option C has incorrect square roots: squaring \(16m-25n\) produces much larger coefficients and a different mixed term. Option D expands to \(16m^2-96mn-25n^2\), so it also fails. The negative middle term tells us that the two terms inside the square must have opposite signs. Memory cue: for a perfect square, check the first square, last square, and twice their product.