I learned difference of squares this week. As the name suggests, we subtract 2 perfect square binomials from each other.

Perfect Square examples: 4, 100, ,

 

We can use this definition to factor the difference of squares:

There is no middle term in Difference of Squares.

Because as we can see they cancels each other.

 

• The first thing we will look at is the minus sign. Because if there is a plus sign, we cannot factor, we call it prime. So there must be minus sign.
• The second thing we will look at is whether the terms are perfect square. If the terms are not perfect square, we cannot factorize them, we call it prime.

And if we decide that the expression is appropriate, we will follow these steps:

 

1- We have to see if there is commonality in the expression. If there is, we first need to divide the expression by the common term.

For example:

We can solve this that way:

After doing this we need to check if there is a minus sign. If so, we are on the right track.

 

2- Let’s say we have such an expression like that:

All we need to do is factor the perfect squares. Since we don’t have a middle term, we don’t need to think about it. The only thing we need to pay attention to is that one of the factors has a plus and the other has a minus. Thus, middle terms can cancel each other.

 

Some examples: