Some patterns in algebra are worth memorizing the way a carpenter memorizes a speed square — and a² − b² = (a + b)(a − b) is the most-used one in the shop. Whenever you spot one perfect square minus another, the factorization writes itself: x² − 9 becomes (x + 3)(x − 3), and 49 − 4y² becomes (7 + 2y)(7 − 2y). It runs in reverse too, which is the real power move: (x + 5)(x − 5) multiplies out to x² − 25 without a single FOIL step, the middle terms always canceling each other out.

The pattern hides in plain sight on tests. A fraction like (x² − 16)/(x − 4) looks unsimplifiable until the numerator factors into (x + 4)(x − 4) and the whole thing collapses to x + 4. Mental-math wizards use it for arithmetic as well: 37² − 33² is ugly to compute directly, but (37 + 33)(37 − 33) = 70 × 4 = 280 in seconds. This calculator verifies the factorization: enter a and b, and it shows a², b², the difference, both factors, and the product check that multiplies them back together — the full round trip from expression to factors and home again.

With the pre-filled defaults — a (first value) 7, b (second value) 3 — the Difference of Two Squares returns a² 49.0000, b² 9.0000, a² - b² 40.0000, Factor 1: (a+b) 10.0000, Factor 2: (a-b) 4.0000, Product check: (a+b)(a-b) 40.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.