Factor perfect squares and differences of squares

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Learn it Two patterns are worth spotting. Difference of squares: a² − b² = (a − b)(a + b), when two perfect squares are subtracted. Perfect-square trinomial: a² + 2ab + b² = (a + b)² and a² − 2ab + b² = (a − b)², when the first and last terms are squares and the middle term is twice the product of their roots. Always take out a common factor first.

Example: Factor 2x² − 50.

Common factor 2: 2(x² − 25).
x² − 25 is a difference of squares: (x − 5)(x + 5).
Answer: 2(x − 5)(x + 5).

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