Difference of Squares

Algebra 1 · Axiom Academy

One perfect square minus another factors instantly. See why with a square you can literally cut apart and rebuild. A difference of squares is a perfect square minus another perfect square. The instant you recognize that shape, you can write the factored form — no guessing. Watch the two squares collapse into a sum times a difference. a^2 and b^2 are both perfect squares the sum times the difference of a and b Why does the pattern work? Think of a^2 as the area of a square with side a , and b^2 as a smaller square with side b . Subtracting b^2 means cutting that smaller square out of a corner . What's left is an L-shaped region whose area is exactly a^2 - b^2 . 3. Rearranged into a Rectangle Cut the L-shape into two strips and slide the lower strip up beside the top one. The pieces fit together into a single rectangle — and the area never changed . Reading off its two sides hands us the factored form directly. The width runs a + b across, and the height stands a - b tall. Same area as the L-shape, so: Applying the pattern is a two-move routine: figure out what's being squared in each term — that's your a and your b — then drop them into (a+b)(a-b) . Watch each problem split into its a and b , then snap into the answer. Recognize both terms as perfect squares. Identify a (the root of the first) and b (the root of the second).

This is the written version of the interactive lesson above. See the full Algebra 1 course.