 # Square of Sum or Perfect Square Trinomials

In this lesson, we will look at the Square of Sum or Perfect 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 x + 1 = 0 ⇒ x = -1 Example 2: x2 + 6x + 9 = 0 x2 + 2(3)x + 32 = 0 (x + 3)2 = 0 x + 3 = 0 ⇒ x = -3

### 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:

Factorize the following:

a) x2 + 8x + 16

b) 4x2– 20x + 25

Solution:

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

How to factor perfect square trinomials?
If we have three terms with perfect square on both ends then try "perfect square trinomial"
Example:
Factor:
1. v2 + 14v + 49
2. t2 + 1/3 t + 1/36
How to factor perfect square trinomials and the difference of two squares?
Example:
Factor each of the following.
a) y2 + 10y + 25
b) 9x2 - 12x + 4
c) 36m2 - 84m + 49
d) 9k2 + 10k + 4
e) y2 - 25
f) 49h2 - 36
g) 32w2 - 18z2
h) 100q2 + 29k2
How to factor a perfect square trinomial?
Examples:
4x2 - 12x + 9
16x2 + 56x + 49
252 - 10x + 1
4x2 + 16x + 16
Factor Perfect Square Trinomials
Example:
x2 + 12x + 36
x2 - 16x + 64
4x2 - 12x + 9
16x2 + 40x + 25

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