Combining Like Terms

What counts as a like term

Two terms are like terms when their variable parts match exactly — same variable, same exponent. $3x$ and $7x$ are like terms. $5x^{2}$ and $2x$ are not, because the exponents differ. $4a$ and $4b$ are not, because the variables differ. Plain numbers (constants) like $8$ and $-3$ are like terms with each other.

The coefficients don't have to match — only the variable parts do. And a variable with no number in front has a coefficient of $1$: the term $b$ means $1b$, and $-x$ means $-1x$. Forgetting that hidden $1$ is the most common slip in this skill.

How to combine

Keep the variable part, and add or subtract the coefficients. $3x + 7x = 10x$ — three $x$'s plus seven more $x$'s is ten $x$'s. The variable never changes and the exponent never changes; only the count in front does. In particular, $3x + 7x$ is not $10x^{2}$.

The sign in front of a term belongs to that term and travels with it. In $9k - 5 - 4k + 2$, the terms are $9k$, $-5$, $-4k$, and $+2$. Group them: $9k - 4k = 5k$ and $-5 + 2 = -3$, so the expression simplifies to $5k - 3$.

More than one variable

When an expression has several variables, sort the terms into groups — all the $a$-terms, all the $b$-terms, all the constants — and combine within each group. The groups never mix: $4a + 6b$ is fully simplified, and it does not become $10ab$. Unlike terms sit side by side in the final answer, connected by their signs.

Worked examples

Try one yourself

Common questions