The Difference of Two Squares — Cheat sheet

Key method

Identify both squares explicitly before substituting. This identity is valid for real or complex values.

Example

For $9x^2-25$, use $A=3x$ and $B=5$ to obtain $(3x-5)(3x+5)$. For $(x+2)^2-9$, use $A=x+2$ and $B=3$:

This avoids an unnecessary expansion.

Avoid this mistake

The sum $A^2+B^2$ does not equal $(A+B)(A-B)$. Over the reals, $x^2+1$ has no linear factors.