Which perfect square is equal to (x^2-2x+1)?

Correct answer: ( (x-1)^2 )

The direct answer is option B: \((x-1)^2\). Use the identity \((a-b)^2=a^2-2ab+b^2\). Taking \(a=x\) and \(b=1\), we get \((x-1)^2=x^2-2x+1\), exactly the given expression. Option A, \((x+1)^2\), expands to \(x^2+2x+1\), so its middle term has the wrong sign. Option B is correct because its expansion gives all three terms, including \(-2x\). Option C, \((x-2)^2\), expands to \(x^2-4x+4\); both the middle coefficient and constant are wrong. Option D, \(x^2-1\), is a difference of squares, but it is not equal to the given expression; it has no \(-2x\) term and has constant \(-1\). The reliable method is to compare the middle term and the last term: the last term 1 suggests the number 1, and the negative middle term tells us to use subtraction. Memory cue: plus inside a square gives a plus middle term, while minus inside gives a minus middle term.