Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Factor a difference of squares
Problem
Factor \(x^{2}-49\) as a difference of squares. Identify both square roots, apply the conjugate identity, and expand the factors to verify the original expression.
Big Picture
What this problem is really about
A difference of squares is recognized by finding a square root for each term and confirming that subtraction lies between them. We’ll place those roots into conjugate binomials with opposite signs, then expand to check that the cross terms cancel and the original expression returns.
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