Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Factor a perfect-square trinomial
Problem
Factor \(x^{2}+10x+25\) as a perfect-square trinomial. Identify the square roots of the first and last terms, verify the middle term as twice their product, and expand the squared binomial.
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What this problem is really about
A perfect-square trinomial must satisfy both the outer-square test and the exact middle-term test. We’ll take the square roots of the first and last terms, verify that twice their product matches the middle term, let that term determine the binomial sign, and expand the square to confirm the pattern.
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