Combining like terms

Counting things of the same kind

Four quarters plus three quarters is seven quarters. Four quarters plus three dimes isn't "seven" of anything: you have to keep them separate.

Monomials work the same way. The variable part tells you what kind of thing you have, and the coefficient tells you how many:

The rule

This is just the distributive property used in reverse: \(4x^2 + 3x^2 = (4 + 3)x^2\).

Subtraction works the same way, because subtracting a term is the same as adding its opposite.

Opposite terms cancel completely: \(5ab - 5ab = 0\).

When terms aren't alike

Unlike terms simply stay as they are. Their sum is written out, and that's a perfectly good final answer. It's a polynomial, which is the topic of the next unit.

Simplifying a long expression

With many terms, a little organization goes a long way. Many students underline or color-code each group of like terms before combining.

Removing parentheses

Before combining, clear any parentheses.

Practice