Combining Like Terms

Ok...so this is your first lesson (I recommend you do them in order if you don't know any, but some things are in the wrong places ^_*).

First, some vocabulary:

Variable: a symbol that stands for a number

Examples: x, y, z, etc.

Terms: variables or numbers separated by addition of subtracting signs

Examples: 1 term - 5x, 4, 3(2x), 56.76x2

2 terms - 5x + 67, x3+ x2, 17 - 18x3

Like Terms: terms with the exact same variable

Examples: x and 4x, 4 and 90, x2 and 56x2

Ok...so now you know the vocabulary...let's get on to combining like terms.

It's pretty easy.  Say you have an expression (contains numbers and/or variables and operation symbols but no equals sign)...

x + 5 - 2x2 + 3x - 9

Let's pick out like terms:
x and 3x
5
and -9 (remember: whether the number is positive or negative depends on the sign before it!)

So, let's add each pair and put them back in the expression.

4x - 2x2 - 4

Now we want to write this in standard form, which is the variable with the highest exponent first, and the exponent number getting smaller as we go to the right.

So this would be:
-2x2 - 4x - 4