Notes
difference of two squares

Difference of Two Squares

The term difference of two squares refers to the identity:

Algebraic Proof

For any numbers $a$ and $b$:

Geometric Interpretation

For $a \gt b$, there is a geometric interpretation of this as a literal difference of two squares. The left-hand side is viewed as the area of a shape made by taking a square of side length $a$ and removing a square of side length $b$ from one corner. The right-hand side is viewed as the area of a rectangle of side lengths $a + b$ and $a - b$. The equality between the two follows from the invariance of area under dissection.