What is the perfect square form of (x^2-18x+81)?

Correct answer: ((x-9)^2)

A perfect square trinomial has the pattern \((a-b)^2=a^2-2ab+b^2\) or \((a+b)^2=a^2+2ab+b^2\). To recognize the pattern, compare the first and last terms with squares and then check whether the middle term equals twice their product, with the correct sign. This prevents confusing a subtraction square with an addition square.

In the expression, \(x^2\) is the square of x and \(81=9^2\). The middle term is \(-18x\), which equals \(-2\cdot x\cdot9\). Hence the expression matches \(x^2-2\cdot x\cdot9+9^2\), so it can be written as \((x-9)^2\). Therefore option A is correct. Expanding it confirms the result: \((x-9)^2=x^2-18x+81\).