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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 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


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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