Difference of Two Squares

Today we looked at factorising using the Difference of Two Squares method. The official mathematical definition of this is as follows:

What this formula is basically saying is, if we have a number (i.e. a) squared and we subtract another number (i.e. b) which has also been squared, we can easily write this in a factorised form (a+b)(a-b). 

This is a little confusing, so i will put a few examples on here, which hopefully may clear it up a little.

Example: Factorise the following: 

a² – 49

This can be written as: a² - 7² 

This is because 49 is actually 7²

We now have "something squared" minus "something else squared", which means we can simply factorise this to be:

(a + 7)(a – 7)  which is our final answer. 

Example: Factorise the following: 

t² – 64

Again, we can see that 64 can be written as 8² 

^{So we now have:} t² - 8²

^{Similarly to the previous example, we have "something squared" minus "something else squared". This means we can factorise this to be:} 

(t + 8)(t – 8) which is our final answer. 

Example: Factorise the following:

(6m)² – (5n)²

Here again, we have "something squared" minus "something else squared". It does look slightly different, but it is still in this same format so we can still factorise using this difference of two squares method. This means it factorises to be: 

(6m + 5n)(6m – 5n)

The following website gives a fantastic description and examples of factorising using the difference of two squares method: http://www.purplemath.com/modules/specfact.htm

I have also posted a worksheet to practice this difference of two squares method under the "Worksheets" tab. 

As always if you do have any questions of concerns feel free to comment on this post or any of the other posts.