Factoring Perfect Square Trinomial

In some cases recognizing some common patterns in the trinomial will help you to factor it faster. For example, we could check whether the trinomial is a perfect square.

Perfect Square Trinomial

A perfect square trinomial is of the form:

(ax)² + 2abx + b²

Take note that

1. The first term and the last term are perfect squares
2. The coefficient of the middle term is twice the square root of the last term multiplied by the square root of the coefficient of the first term.

When we factor a perfect square trinomial, we will get

(ax)² + 2abx + b² = (ax + b)²

 

The perfect square trinomial can also be in the form:

(ax)² – 2abx + b²

In which case it will factor as follows:

(ax)² – 2abx + b² = (ax – b)²

Example 1:	x2 + 2x + 1 = 0
	(x + 1)2 = 0
Example 2:	x2 + 6x + 9 = 0
	x2 + 2(3)x + 32 = 0
	(x + 3)2 = 0

Example:

Factor the following trinomials:

a) x² + 8x + 16
b) 4x²– 20x + 25

Solution:

a) x² + 8x + 16
= x² + 2(x)(4) + 4²
= (x + 4)²

b) 4x²– 20x + 25
= (2x)²– 2(2x)(5) + 5²
= (2x – 5)²

Videos

The following video shows how to factor perfect square trinomials.

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