Difference+of+Squares

Difference of Squares

A difference of squares is one the of many types of factoring for quadratic expressions. But this type is the easiest to identify and to factor down. There are several steps in using this method.

**__Step 1__** First you have to recognize that it is a difference of squares. The way to do that is to look for the generic expression of **a 2 - b 2 **. Once you have spotted this, it is relatively easy to factor a difference of squares.

**__Step 2__** After you have identified that it is in fact a difference of squares the next step is to break it down into two separate quantities. First, you have to break down the "a" term into its root and place it into the first spot of each quantity. Then you break down the "b" term into its root and do the same. .

__**Step 3**__ Once you have broken each term and placed them in the quantities, the quantities have to have different signs. They have different signs because the signs cancel out the middle term and allows it to only become a 2 term equation.

**__Examples__** 100x 2 - 49 Break down both terms and separate them by different signs (10x + 7)(10x - 7)

16x 2 - 25 Find the root of both terms and then place them in the 2 quantities and seperate them by different signs.

If it was done correctly then your answer should be as follows: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 130%;">(4x + 5) (4x - 5)

Here is a little video that will help even more. media type="youtube" key="pgEzlCwAJVY" height="315" width="420"