The identity a² − b² = (a + b)(a − b) is one of the fastest factoring patterns in algebra.
About this calculator
The identity a² − b² = (a + b)(a − b) is one of the fastest factoring patterns in algebra. For a = 7 and b = 3: 49 − 9 = 40, and (7 + 3)(7 − 3) = 10 × 4 = 40.
Spot this pattern whenever you see a perfect square minus another — x² − 16 factors to (x + 4)(x − 4). It also runs backward: multiply (a + b)(a − b) to expand without FOIL errors.
Pair with [[foil-method]] for expanding binomials, [[completing-the-square]] for quadratics, and [[square]] to compute a² and b² separately.
Common uses
- Factor x² − 16 as (x + 4)(x − 4)
- Verify 7² − 3² = 40 quickly
- Check factoring homework before submitting
- Expand (a + b)(a − b) without FOIL mistakes
- Simplify expressions like 25 − 9 in one step
Frequently asked questions
What is 7² minus 3²?
49 − 9 = 40. Factored: (7 + 3)(7 − 3) = 10 × 4 = 40.
How do you factor x² − 16?
x² − 16 = (x + 4)(x − 4). Here a = x and b = 4 because 16 = 4².
Does order matter for a and b?
a² − b² equals b² − a² multiplied by −1. The factored form uses (a + b)(a − b) with consistent a as the first square.
Can this identity help with mental math?
Yes. 52² − 48² = (52 + 48)(52 − 48) = 100 × 4 = 400 without squaring each term separately.