Combining Like Terms

Q: What happens to the sign in front of a term?

It belongs to the term and moves with it. In $9y + 2 - 4y$, the middle of the expression contains $-4y$, not $4y$ — so the $y$-terms combine to $9y - 4y = 5y$. Reading each term with its sign is the whole trick.

An expression like $7a + 5b - 3a + b$ is built from terms — the pieces separated by plus and minus signs. Like terms are terms with the exact same variable part: $7a$ and $3a$ are like terms, and $5b$ and $b$ are like terms. Combining like terms means merging each matching group into a single term, shrinking the expression down to $4a + 6b$ .

This is the basic cleanup move of algebra. You'll use it every time you simplify an expression, and it's the first step in solving most multi-step equations. The rule is short: same variable, same exponent — then add or subtract the coefficients.

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

Example 1: one variable

Combine like terms: $5x + 3x$ .

Both terms have the same variable part,

x

5x + 3x

Add the coefficients and keep the variable

(5 + 3)x = 8x

Answer: $8x$

Example 2: variable terms and constants

Simplify $8m + 4 - 3m + 6$ .

Start with the expression

8m + 4 - 3m + 6

Group the

m

-terms

8m - 3m = 5m

Group the constants

4 + 6 = 10

Write the simplified expression

5m + 10

Answer: $5m + 10$

Example 3: two variables and a hidden 1

Simplify $6a + 2b - a + 5b$ .

Start with the expression — remember

-a

means

-1a

6a + 2b - a + 5b

Group the

a

-terms

6a - 1a = 5a

Group the

b

-terms

2b + 5b = 7b

Write the simplified expression

5a + 7b

Answer: $5a + 7b$

Example 4: exponents must match

Simplify $4x^{2} + 3x - x^{2} + 6x$ .

Start with the expression

4x^{2} + 3x - x^{2} + 6x

Group the

x^{2}

-terms

4x^{2} - 1x^{2} = 3x^{2}

Group the

x

-terms

3x + 6x = 9x

The two groups are unlike, so they stay separate

3x^{2} + 9x

Answer: $3x^{2} + 9x$

Try one yourself

Common questions

Can I combine

5x

and

5x^{2}

No. Like terms need the same variable raised to the same power, and $x$ and $x^{2}$ are different powers. Matching coefficients don't matter — $5x + 5x^{2}$ is already as simple as it gets.

What happens to the sign in front of a term?

It belongs to the term and moves with it. In $9y + 2 - 4y$ , the middle of the expression contains $-4y$ , not $4y$ — so the $y$ -terms combine to $9y - 4y = 5y$ . Reading each term with its sign is the whole trick.

Are

7

and

7x

like terms?

No. $7$ is a constant and $7x$ has a variable, so they can never merge. An answer like $5y + 7$ is fully simplified — a variable term and a plain number always stay separate.

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Combining Like Terms

What counts as a like term

How to combine

More than one variable

Worked examples

Example 1: one variable

Example 2: variable terms and constants

Example 3: two variables and a hidden 1

Example 4: exponents must match

Try one yourself

Common questions

Keep learning

The Distributive Property

One-Step Equations (Add / Subtract)

Two-Step Equations