Simplifying algebraic expressions with one or more variables by combining like terms is what this lesson will show you.
Learning first to simplify numerical expressions will make it easier to understand how to simplify algebraic expressions.
Let's say you want to simplify 5 + 5 + 5 + 5. What is a quick way to get the answer?
You can do 4 × 5 and 4 × 5 is a simplified version of 5 + 5 + 5 + 5.
If you had the following problem to simplify 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5, you can quickly see why it would be useful to just count how many fives there are and then times the amount by 5.
Since there are 11 fives, the simplified expression is 11 × 5
Try to simplify v + v + v + v + v + v
Well, in the same manner, just count how many v's there are and multiply the amount by v.
Since there are 6 of them, v + v + v + v + v + v = 6 × v.
To simplify 6 × v even further, you can write 6v. However, remember that there is a multiplication between 6 and v.
Notice that putting a 1 next to each v will not change the answer.
v + v + v + v + v + v = 1v + 1v + 1v + 1v + 1v + 1v = ( 1 + 1 + 1 + 1 + 1 + 1)v = 6v
This shows you a couple of things. First, 1v = v.
Then, when simplifying algebraic expressions, you can just do your math with the number on the left on the variable.
Now, try to add v + v + v + v + x + x + x
I hope it makes sense to you that you cannot add v and x. What is v + x? You cannot say 2v because it is v + v that is equal to 2v.
You cannot say 2x because it is x + x that is equal to 2x. Basically v and x are not like terms, so v + x is just equal to v + x.
By the same token, there is another thing you need to watch for. What is v + 2? It is not 2v as already shown.
Again, v and 2 are not like terms either, so v + 2 = v + 2
However, since you can add all the vs, we call the vs like terms. Same for the xs, they are called like terms.
v + v + v + v + x + x + x = ( v + v + v + v) + ( x + x + x) = 4 × v + 3 × x = 4v + 3x
What about 4v + 3x + 5v + 4x?
You cannot add 4v to 3x, but you can add 4v to 5v. And you can add 3x to 4x
4v + 3x + 5v + 4x = 4v + 5v + 3x + 4x = 9v + 7x
When simplifying algebraic expressions, subtraction and/or putting negative numbers work pretty much the same. You can only subtract like terms. The only difficulty you will encounter is the subtraction or addition of integers.
May 01, 23 07:00 AM
Apr 24, 23 07:02 AM