In this unit’s final lesson, we’ll learn how to quickly factor **general form** **quadratics** that are considered **“perfect square trinomials”** (PST). In a PST, the first and last term of these trinomials are always **perfect squares**. If you don’t recognize the pattern of a PST, you could still factor the quadratic normally by **trial-and-error **or by **decomposition**. Therefore, remembering this technique isn’t technically required but if you do recognize the pattern, consider it a shortcut.

Examples of a perfect square trinomials are:

- y =
**x²**+ 6x +**9**- Here,
**√x² =**x and**√9 = 3** - This factors into (
**x**+**3**)²

- Here,
- y = 4x² +28x + 49
- Here,
**√4x² =**2x and**√49 = 7** - This factors into (
**2x**+**7**)²

- Here,

Two more examples of factoring perfect square trinomials are shown in the video below.

Take-home message:You can factor a perfect square trinomial as:

- a² + 2ab + b² = (a + b)²
- a² – 2ab + b² = (a – b)²