Perfect Squares — Cheat sheet

Key method

A repeated linear factor gives a repeated zero. Its graph touches the horizontal axis rather than crossing there.

Example

In $4x^2-12x+9$, the outer terms are $(2x)^2$ and $3^2$, and $-12x=-2(2x)(3)$. Therefore

Its only zero is $x=3/2$, with multiplicity two; its value cannot be negative.

Avoid this mistake

$A^2+B^2$ is missing the mixed term and is not $(A+B)^2$.