Difference of Squares: How to Factor a² − b²
Factor a difference of squares with two worked examples and the mistakes to avoid.
The pattern
- a² − b² = (a − b)(a + b)
Two perfect squares with a minus sign between them.
Example 1
Factor x² − 49
- x² = x · x and 49 = 7 · 7
- a = x, b = 7
(x − 7)(x + 7)
Example 2
Factor 4x² − 25
- 4x² = (2x)² and 25 = 5²
- a = 2x, b = 5
(2x − 5)(2x + 5)
Common mistake
x² − 49 = (x − 7)²
(x − 7)² has a middle term −14x, so it is not the same.
A sum of squares like x² + 49 does not factor over the real numbers.
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