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Factoring Quadratic

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

For example: Square of Sum, Square of Difference and Difference of Two Squares

 

 

Square Of Sum

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
   
Example 2:

x2 + 6x + 9 = 0

  x2 + 2(3)x + 32 = 0
  (x + 3)2 = 0
  x = -1

 

 

Square of Difference

A square of difference is a type of quadratic equations of the form:

x2 – 2bx + b2 = (xb)2

Example 1: x2 – 2x + 1 = 0
  (x – 1)2 = 0
  x=1
   
Example 2:

x2 – 6x + 9 = 0

  x2 – 2(3)x + 32 = 0
  (x – 3)2 = 0
  x 3 = 0 ⇒ x = 3

 

 

Difference of Two Squares

A difference of two squares is a type of quadratic equations of the form:

(a + b)(a – b) = a2b2

Example: x2 – 25 = 0
  x2 – 52 = 0
  (x + 5)(x – 5) = 0
   

We get two values for x:

  x = -5, x = 5

Be careful! This method only works for difference of two squares and not for the sum of two squares: a2 + b2 ≠ (a + b)(ab)

 

 

Videos

The following videos explain how to factor a difference of squares.

Two Factoring Shortcuts in Algebra - Learn two helpful shortcuts for factoring quadratic equations. Save trial-and-error time on tests.

 

 

 

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More Algebra Help at MathWorld
 

 

 

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