Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Factor completely using a GCF and another pattern
Problem
Factor \(3x^{2}-27\) completely. First extract the numerical GCF exactly once, then factor the remaining difference of squares into conjugates and expand to verify.
Big Picture
What this problem is really about
Complete factoring can require more than one pattern, so the greatest common factor comes first. We’ll extract it exactly once, inspect the remaining binomial for a difference of squares, split that remainder into conjugates, and expand through both stages to check that no factor was duplicated.
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