A model arranges \(25x^2-30x+9\) as a square. Which is the correct side?

Correct answer: \(5x-3\)

The direct answer is C, \(5x-3\). To identify a square side, take the square roots of the first and last terms: \(25x^2=(5x)^2\) and \(9=3^2\). The expression must therefore have the form \((5x\pm3)^2\). Check the middle term. Using \((u-v)^2=u^2-2uv+v^2\), \((5x-3)^2=25x^2-2(5x)(3)+9=25x^2-30x+9\), exactly as required. A gives a positive middle term, \(+30x\), so its sign is wrong. B does not square to the required leading term and is not the appropriate binomial side. D would produce a constant term 81 and middle term \(-90x\), both incorrect. Memory cue: take the roots of the end terms, then use the middle-term sign to choose plus or minus.