Can I combine 3x and 2x^2?

No. Even though both contain the variable x, the exponents are different: x^1 versus x^2. You can only combine terms that have the same variable with the same exponent (called like terms). 3x and 2x^2 must stay separate.

Why do we combine like terms?

Combining like terms simplifies an expression, making it shorter and easier to work with. For example, 5x + 3 + 2x + 7 is much easier to solve once you simplify it to 7x + 10. Simpler expressions mean fewer chances for mistakes in later steps.

What if a coefficient is negative?

Negative coefficients combine just like positive ones. The expression 5x - 3x means 5x + (-3x) = (5 - 3)x = 2x. Always keep the sign attached to each coefficient as you add them together.

What happens when I combine x and -x?

These terms have coefficients of 1 and -1. When combined: 1x + (-1x) = (1 - 1)x = 0x = 0. The two terms cancel out completely, and the entire expression becomes zero.

Combining Like Terms

Combining like terms merges coefficients of identical variables to simplify expressions and solve equations more efficiently.

ax + bx = (a + b)x

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What each symbol means

What Combining Like Terms takes

Symbol	Meaning
$a$	The numerical coefficient of the first term—the number multiplying $x$ ; if confused with an exponent, you might incorrectly write $(a+b)^x$ instead of $(a+b)x$ .
$b$	The numerical coefficient of the second term—the number multiplying the same variable $x$ ; terms can only combine if $b$ multiplies an identical variable and exponent as $a$ does.
$x$	The variable (the letter) that appears in both terms; the exponents must be identical—for example, $3x^2$ and $5x$ cannot be combined because the exponents differ.

When to use it

Reach for this when you have multiple terms containing the same variable and exponent, and you want to simplify the expression.

Level

Usually taught in: Algebra I

Worked examples

1. Simplify two like terms with small positive integers

Problem

Simplify

3x + 2x

$3x + 2x$
Write both terms; notice that each contains the variable $x$ with the same exponent (implicitly 1).
$= (3 + 2)x$
Apply the distributive property: factor out $x$ and group the coefficients together.
$= 5x$
Add the coefficients: $3 + 2 = 5$ .

Answer: $5x$

Both terms share the variable $x$ , making them like terms. The distributive property lets us factor out $x$ and add the coefficients, simplifying to $5x$ .

2. Combine three terms with negative coefficients

Problem

Simplify

-4x + 7x - 2x

$-4x + 7x - 2x$
Write all three terms, each containing $x$ ; note that the first coefficient is negative and the third is being subtracted.
$= (-4 + 7 - 2)x$
Factor out $x$ by grouping all coefficients, keeping track of their signs: $-4$ , $+7$ , and $-2$ .
$= (3 - 2)x$
First, combine $-4 + 7 = 3$ ; now we must compute $3 - 2$ .
$= x$
Complete the arithmetic: $3 - 2 = 1$ , and a coefficient of 1 is written as just $x$ , not $1x$ .

Answer: $x$

With three like terms and negative coefficients, we combine all coefficients by adding them (treating signs as part of each) to get 1. A coefficient of 1 is not written explicitly.

3. Real-world problem: revenue from a bake sale

Problem

At a bake sale, brownies sell for

x

dollars each. On Monday you sold 12 brownies, on Tuesday 8 brownies, and on Wednesday 15 brownies. Write and simplify an expression for your total revenue.

$12x + 8x + 15x$
Represent revenue for each day: 12 brownies at $x$ dollars each, plus 8 at $x$ each, plus 15 at $x$ each.
$= (12 + 8 + 15)x$
All three terms are like terms because each has the variable $x$ ; factor out $x$ by grouping the quantities.
$= 35x$
Add the coefficients: $12 + 8 = 20$ , then $20 + 15 = 35$ .

Answer: $35x$

Each day's revenue has the same variable $x$ (the price per brownie), so we combine them by adding the quantities. The simplified expression $35x$ represents selling 35 brownies total at $x$ dollars each.

Common mistakes

Where Combining Like Terms usually goes wrong

The mistake	Why it is wrong	The fix
$3x + 2y = 5xy$	The variables $x$ and $y$ are different, so these are not like terms and cannot be combined.	$3x + 2y$ cannot be simplified; the terms must stay separate.
$2x^2 + 3x = 5x^2$	Although both terms contain $x$ , the exponents differ ( $x^2$ versus $x^1$ ), so $2x^2$ and $3x$ are not like terms.	$2x^2 + 3x$ remains unchanged; the terms cannot be combined.
$5x + 3 = 8x$	The term 3 is a constant with no variable, so it is not a like term with $5x$ and cannot be combined with it.	$5x + 3$ stays as written; the constant and variable term remain separate.

Tips and when to use something else

Always check that variables and exponents match before combining— $3x^2$ and $5x$ look similar but cannot be combined because the exponents differ.
Treat subtraction as adding a negative: $6x - 2x = 6x + (-2x) = 4x$ , so the second coefficient carries its negative sign.
If you have parentheses like $3(x + 2) + 2x$ , use the Distributive Property first to expand, then combine like terms.
If a coefficient becomes 1, omit it: $1x = x$ . If a coefficient becomes 0, the term vanishes: $3x - 3x = 0$ .

Related formulas

Distributive PropertyThe Distributive Property lets you multiply a number by a sum or difference by distributing the multiplication to each term separately.Order of OperationsOrder of Operations is the set of rules that tells you which calculation to do first when you have multiple operations in one expression.Commutative PropertyThe Commutative Property says you can switch the order of numbers when adding or multiplying without changing the result.

Frequently asked questions

Can I combine $3x$ and $2x^2$ ?: No. Even though both contain the variable $x$ , the exponents are different: $x^1$ versus $x^2$ . You can only combine terms that have the same variable with the same exponent (called like terms). $3x$ and $2x^2$ must stay separate.
Why do we combine like terms?: Combining like terms simplifies an expression, making it shorter and easier to work with. For example, $5x + 3 + 2x + 7$ is much easier to solve once you simplify it to $7x + 10$ . Simpler expressions mean fewer chances for mistakes in later steps.
What if a coefficient is negative?: Negative coefficients combine just like positive ones. The expression $5x - 3x$ means $5x + (-3x) = (5 - 3)x = 2x$ . Always keep the sign attached to each coefficient as you add them together.
What happens when I combine $x$ and $-x$ ?: These terms have coefficients of $1$ and $-1$ . When combined: $1x + (-1x) = (1 - 1)x = 0x = 0$ . The two terms cancel out completely, and the entire expression becomes zero.

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Reviewed 2026-09-18