Factor a Perfect Square Trinomial

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:

  1. y = + 6x + 9
    • Here, √x² = x and √9 = 3
    • This factors into (x + 3
  2. y = 4x² +28x + 49
    • Here, √4x² = 2x and √49 = 7 
    • This factors into (2x + 7

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