Combining Like Terms
For example, say you have the expression 3x + 5x + 7y + 9x - 4y.
This expression looks a bit confusing, but we can combine common terms to make it much simpler.
To be a common term, the term must have the same variable and the same exponents.
When you combine like terms, be sure to use the + or - that is in front of the coefficient, or number in before the letter.
So in this case, we will add the 3, 5 and 9 that is in front of the x terms. Then we will subtract 7 and 4 that is in front of the y terms.
3x + 5x + 7y + 9x - 4y = 17x + 3y
Here are a few more examples:
1.) 7m + 14m - 6n - 5n + 2m
Step 1: Organize your like terms. You can use a highlighter, shapes, or just rewrite the problem so that the like terms are next to each other.
7m + 14m - 6n - 5n + 2m
Step 2: Combine the coefficients.
(7 + 14 + 2)m + (-6 + -5)n
23m - 11n
2.) 5h + 11g + h - 8g
Step 1: Organize your like terms.
5h + 11g + h - 8g
Step 2: Combine the coefficients.
When you have a variable that does not have a coefficient, you may write
in a 1 to help you.
5h + 11g + 1h - 8g
(5 + 1)h + (11 - 8)g
6h + 3g
3.) 5x + 8x + 10x2 - 7x2 - 4x
Step 1: Organize your like terms.
This problem often leads to a common mistake. Just because they all
have x in them does not mean that they are all like terms.
The variable AND the exponent must be the same.
5x + 8x + 10x2 - 7x2 - 4x
Step 2: Combine the coefficients
(5 + 8 - 4)x + (10 - 7)x2
9x + 3x2
Related Links:
Combining Like Terms Worksheets
Combining Like Terms Quiz
Algebraic Expressions
Math
Fractions
Factors