Chapter 9: Adding and Subtracting with Variables 113
CHECK POINT
Label each pair of terms like or unlike.
- 7y^2 and 11y
- 3t^2 and 5t^2
- 2x and 7x
9. -9a^2 and -15a^3
10. 132x^3 and -83x^3
Adding and Subtracting Like Terms
So x + x is 2x, but x + y must stay as x + y because we have no way to combine the unlike terms.
What about 2x + 3x? The variable is the same, but the coefficients, the numbers in front, are
different. Is that a problem? Like terms are terms that have the same variable and the same
exponent. These terms meet that rule, so why is it okay for the coefficients to be different?
Think about what the coefficients tell you. You have 2 x’s and another 3 x’s. That’s all x’s, so
you can combine them. The 2x means x + x and the 3x means x + x + x. You can put them all
together and end up with a total of 5 x’s. 2x + 3x = 5x.
If the variable parts of two terms are identical, you can add them by just adding the coefficients.
As long as you have the same variable and same exponent, you can just look at the coefficients to
tell you how many you have.
There’s no change to the variable part. You’re just changing the count of how many of that
variable you have. The variable portions tell you that you’re working with the same kinds of
things, and the coefficients tell you how many of them you have. If you were asked to add 7 cars
and 5 cars, you’d get 12 cars, not 12 cars squared. 8 apples minus 3 apples gives you 5 apples. The
cars or apples don’t change. When you add or subtract like terms, only the number changes.
2 x
5 x
1
5
3 x
