Square of Sum or Perfect Square Trinomials

In some cases recognizing some common patterns in the quadratic equation will help you to factorize the quadratic.

In this lesson, we aill look at the Square of Sum or Perferct Square Trinomials.

A Square of Sum is a type of quadratic equations of the form:

x² + 2bx + b² = (x + 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

Perfect Square Trinomials

We may check the pattern of the expression to determine whether it is a Perfect Square Trinomial, namely,

p² + 2pq + q² = ( p + q )² or

p²– 2 pq + q² = ( p – q )²

Example:

Factorise the following:

a) x² + 8x + 16

b) 4x²– 20x + 25

a) x² + 8x + 16

= x² + 2(x)(4) + 4 2 ← Write in the form of p² + 2pq + q²

= (x + 4)²

b) 4x²– 20x + 25

= (2x)²– 2(2x)(5) + 5² ← Write in the form of p² + 2pq + q²

= (2x – 5)²

This video shows hoe to factor perfect square trinomials.

This video will demonstrate how to factor perfect square trinomials and the difference of two squares.

The following video shows an example of the Square of a Sum

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