Thursday, July 11, 2013

Collecting Like Terms

Just because a problem asks you to add (or subtract) terms, doesn't mean we can...

When simplifying or solving algebraic expressions we have to know when we can collect terms and when we can't.

We can only collect (or add/subtract) LIKE terms.  So what are LIKE terms???

Terms are considered to be like terms if they have the same variable (or letter component) and the same exponent.  Let's look at the lists below and see how some terms are like terms and some terms are not.

If we look at the column of Like terms, we can see that the leading number (also known as the coefficient) can be anything, but the letters (variables) and the exponent (or power on the variable) must be identical. Like terms can be added or subtracted from one another (I like to think of them as being in the same family)!

If we look at the column of unlike terms, we can see that either the variables are different or the exponents are different. Unlike terms can not be added or subtracted from one another!!

 For example - when we see a problem like this, it looks like they want us to add and subtract all of these terms and come up with one term as the answer... but we can't!:
 3xy - 4xy + 2xyz

There are two terms that are alike and one that is not alike.  The positive 3xy and the negative 4xy have identical variables and exponents (remember that if no exponent is visible, then the variable is raised to an invisible 1).  The term 2xyz has that extra "z" in its variable, and so it is not identical to the other two terms.

When we collect like terms, we let the numbers and signs do the work, and we bring the variables along.  A positive 3xy and a negative 4xy have different signs, so we will subtract the numbers and keep the sign of the bigger number (the 4 is bigger than the 3, so the negative sign wins).  The difference between 3 and 4 is 1.  So 3xy -4xy = -1xy.

The problem can be simplified to -1xy + 2xyz.  We can't add these last two terms together because they are not LIKE terms.

There is a great video about collecting like terms at Khan Academy (click here).  When the link takes you to Khan Academy there are actually several good videos entitled "collecting like terms", you should watch them all!!  Then there are practice problems you can try (click here).

Knowing when and how to collect like terms is going to very important to succeeding in Algebra!

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