Which perfect square equals (x^2-14x+49)?

Correct answer: ((x-7)^2)

The direct answer is option D: \((x-7)^2\). Use \((a-b)^2=a^2-2ab+b^2\) with \(a=x\) and \(b=7\). This gives \((x-7)^2=x^2-2\cdot x\cdot7+7^2=x^2-14x+49\), exactly the given expression. Option A, \((x+7)^2\), would have a positive middle term \(+14x\). Option B, \((x-14)^2\), would expand to \(x^2-28x+196\), so both its middle and constant terms are wrong. Option C, \((x+14)^2\), would give \(x^2+28x+196\). Option D has the correct square term, negative middle term, and positive constant. Memory cue: a negative middle term in a perfect square means the bracket uses subtraction.