Choose the factorised form of (x^2-4xy+4y^2-25).

Correct answer: ((x-2y-5)(x-2y+5))

The direct answer is A: \(x-2y-5)(x-2y+5)\). First, \(x^2-4xy+4y^2=(x-2y)^2\), because the middle term is \(-2(x)(2y)=-4xy\). Therefore the full expression is \((x-2y)^2-25=(x-2y)^2-5^2\). The difference-of-squares identity gives option A. Option B uses \(x+2y\), which would produce a positive \(4xy\). Option C is only an intermediate form, not fully factorised into two factors. Option D does not have equal square roots and expands incorrectly. Thus A is the complete correct factorisation. Find the perfect-square trinomial before factoring the final difference.