If a + b = 7 and a − b = 3, find a² − b²:

By the identity a² − b² = (a + b)(a − b) = 7 × 3 = 21. (No need to find a and b separately!) For curiosity: solving gives a = 5, b = 2, and 5² − 2² = 25 − 4 = 21 ✓.