Objectives 

• Greatest Common Factor

• Special Factoring Techniques

• Factoring by Grouping

Examples

• Example 1

• Example 2

• Example 3

• Example 4

For example,  factors as  .

The key here is to find two numbers whose product is 8 and whose 
sum is 6.  So we use 4 and 2.

Notice here that multiplying out the factored form produces the original expression.

Using the technique descibed above,  factors as  . 

This type of expression is called a "difference of squares."

Notice that, in this case,  the "middle term" disappears when you multiply these two factors.

Special Note: In fact, a difference of squares will always factor according to the rule: 

Another example is: 

Warning: When working with real numbers, a "sum of squares" will not factor according to this rule (or any other rule).

Try it on  .

We have just seen that a difference of squares always factors. The same is true for a "difference of cubes."

For example: 

The general rule for a "difference of cubes" is: 

Remember, you can verify this rule by multiplying out the factored form.

Note: Although a sum of squares will not factor, a "sum of cubes" will factor, for example,

.

The general rule for a "sum of cubes" is: