Products and Factors
5-5Differences of Two Squares
Overview
a^2 − b^2 = (a − b)(a + b). Recognize perfect squares to factor instantly.
Key ideas
- Two terms, both perfect squares, separated by a minus.
- (a − b)(a + b) on factoring.
- Sums of squares don’t factor over reals.
Worked examples
Example 1
Problem. Factor x^2 − 16.
Solution. (x − 4)(x + 4)
Example 2
Problem. Factor 9a^2 − 25.
Solution. (3a − 5)(3a + 5)
Practice
Try each one. Click Show answer when ready.
- 1.
Factor x^2 − 49.
- 2.
Factor 4y^2 − 1.
- 3.
Factor 25 − m^2.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Factor: 49x² − 81y².
- 2.
Factor: 16a⁴ − 25b².