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Difference of squares

Factoring Quadratics

Let's look at three methods for factoring quadratic equations.

The three methods are:


Factoring Trinomials

Difference of Squares

Step 1. Check to see if you can factor out a greatest common factor. If there is not a GCF then move to step 2

            3x^3 -2x^2 +6x-4

Step 2. Create smaller groups by grouping the 1st two terms, and the 2nd two terms
             3x^3 -2x^2 +6x-4

Step 3. Factor out the Greatest Common Factor (GCF)
            x(3x-2) + 2(3x-2)

Step 4. Factor out any perfect matches,and rewrite what is remaining. In this                        example you have a perfect match of (3x-2) so you can factor this match                 out. 
            Rewrite = (3x-2)(x+2)

For many examples of grouping see: Factoring by groupimg

factoring by grouping
factoring by grouping (x+1)(7x+11)
grouping a method of factoring (x+11)(7x-1)
This could be called the FOIL method and is helpful with difficult trinomials. 
These first terms in the parenthesis must equal the first term,when multiplied together.
Next,you have to decide on the second term for the parenthesis. The terms must equal the middle term when they are multiplied together.
The terms equal 76x therefore,use this combination
Video Guide
0:19 x^2 + 3x-18 

1:49 a^2-13a-48 

The pattern equals a^2 -b^2

Example: 4x^2 -25
Step 1 Take the square of each term and plug them into the pattern

(2x +5)(2x-5)

x^2 -36
Take the square of each term and follow the pattern

Factoring by Grouping

Factoring Trinomials