Like Terms

We are now looking at like terms in algebra.

Firstly, we have to remember what a term is. A term is a number, a pronumeral, or a combination of both of these. For example, 4 is a term, x is a term, and 3abxyz is also a term. When we write an algebraic expression, terms are easy to spot because they are always seperated by a "+" or a "-". For example, in the expression;

2ab + 4c - 6 - x

our terms are 2ab, 4c, -6, and -x.

Now like terms are special terms. These are terms that have EXACTLY the same combination of pronumerals (letters). For example, 2a and 4a are like terms, because they both have just the pronumeral "a". However, 4b and 5bc are NOT like terms. They both do have a "b" in them, however the 5bc also contains a "c" so the combination of pronumerals is different.  

If we have a look at an expression now; 

4a + 2ab + 5 - a + 3ab - 1

We can go and collect like terms in this, so the like terms would be:

• 4a and -a
• 2ab and 3ab
• 5 and -1 

Once we have collected the like terms in an expression, we can do a process called simplification (or simplifying) where we combine these like terms and write the expression in a simpler, shorter way. So again looking at the expression above, if we were to combine the like terms we would get:

• 4a and -a becoming 3a, because we start with 4 lots of a and then take 1 lot of a away, leaving us with 3 lots of a, or 3a. 
• 2ab and 3ab becoming 5ab, because we start with 2 lots of ab and add 3 more lots of ab, leaving us with 5 lots of ab, or 5ab. 
• 5 and -1 becoming 4, because we start with 5 and take 1 away, leaving us with 4. 

We can then write our expression with the combined like terms instead of all of the original terms. The new expression would look like; 

3a + 5ab + 4

Which as you can see is much simpler and much shorter than the previous expression. We have now simplified the expression. 

Now a few points to remember when doing these questions is that when we are looking at these expressions and like terms; 

1. Don't worry about the coefficient (the number out the front of the term, so the 4 in 4ax). When we look at identifying like terms, we are just looking at the pronumerals. Once you have identified the like terms, you can then look at the coefficients and use these to combine your like terms. 
2. The order of the pronumerals does not matter. xy is the same as yx, so 4xy and 3yx would be like terms. If you really think about it, the combination of pronumerals in these terms is still the same. They both have an "x" and they both have a "y", so they must be like terms. 

I have uploaded a worksheet for this into the "Worksheets" tab. Work through this now for class work and homework. The first page is the most important work. The second page contains extra questions to work through if you have time. Remember to check your answers with the answers provided. 

If you have any questions feel free to comment on this post, or email or chat to me in person.