How to spot like terms, combine them, and simplify expressions that include brackets, negative signs, exponents, and fractions.
What are like terms?
Like terms are terms with the same variable raised to the same power. 3x and −7x are like terms. 4x² and x² are like terms. But 3x and 3x² are not, because the powers are different.
Plain numbers, called constants, are like terms with each other: 5 and −2 can be combined. The number in front of a variable is its coefficient. When there’s no number shown, as in x, the coefficient is 1.
How do you combine like terms?
Combining like terms means adding or subtracting their coefficients and keeping the variable part unchanged. So 5x + 3x = 8x, because 5 + 3 = 8 and the x stays the same.
It works because of the distributive property: 5x + 3x is the same as (5 + 3)x. You’re counting how many x’s you have. Five of something plus three more of the same thing is eight of it.
- Clear any brackets by distributing.
- Mark each term together with the sign in front of it.
- Group terms with the same variable and power.
- Add or subtract the coefficients in each group.
- Write the result in descending order of power, constants last.
What does a basic example look like?
Simplify 3x + 5 − x + 2. The x terms are 3x and −x. The constants are 5 and 2.
Combine the x terms: 3x − x = 2x, since x means 1x and 3 − 1 = 2. Combine the constants: 5 + 2 = 7. The simplified expression is 2x + 7.
That’s as far as it goes. 2x and 7 aren’t like terms, so they stay separate. Writing 9x here is a mistake people make when they want the answer to be “one thing.”
How do you simplify expressions with brackets?
Distribute first, then combine like terms. Brackets have to go before you can see which terms match.
Simplify 2(3x − 4) − (x − 5). Distribute the 2 to get 6x − 8. The minus in front of the second bracket works like multiplying by −1, so −(x − 5) becomes −x + 5. Now you have 6x − 8 − x + 5.
Combine: 6x − x = 5x and −8 + 5 = −3. The answer is 5x − 3. Simplifying expressions with brackets is mostly about that minus sign, which is easy to apply to the first term and forget for the second.
How do negative signs work when combining terms?
Each term owns the sign directly in front of it. Read 12x − 4 − 5x + 9 as 12x, −4, −5x, and +9.
Grouping them: 12x + (−5x) = 7x, and −4 + 9 = 5. The result is 7x + 5. Some students find it helps to circle each term with its sign before moving anything.
Another example: 7 − 2(x − 3) + 4x. The −2 multiplies both terms inside, giving −2x + 6. Then 7 − 2x + 6 + 4x simplifies to 2x + 13.
How do you combine like terms with exponents?
Only combine terms whose powers match exactly. x² terms go with x² terms, x terms with x terms, and constants with constants. The exponent itself never changes when you add.
Simplify 4x² + 3x − 2x² + x − 6. The x² group gives 4x² − 2x² = 2x². The x group gives 3x + x = 4x. The constant is −6. The answer is 2x² + 4x − 6.
A frequent slip is turning 3x² + 2x² into 5x⁴. Adding like terms adds the coefficients only, so the answer is 5x². Exponents add when you multiply, as in x² × x² = x⁴, not when you add.
How do you combine like terms with fractions?
Add the fractional coefficients the same way you’d add any fractions, using a common denominator.
For x/2 + x/3, the coefficients are 1/2 and 1/3. With a common denominator of 6, that’s 3/6 + 2/6 = 5/6. So x/2 + x/3 = (5/6)x. The fraction calculator can help with the coefficient arithmetic if the denominators are awkward.
Decimals are easier still. 0.5x + 1.25x is 1.75x, because 0.5 + 1.25 = 1.75. Keep the decimal or convert it to a fraction, whichever your class prefers, and don’t round partway through. The combine like terms calculator gives exact fractions, so it shows this one as (7/4)x, which is the same value.
What about expressions with more than one variable?
The same rule applies: the whole variable part must match. In 5a − 3b + 2a + 7b − 4, combine 5a + 2a = 7a and −3b + 7b = 4b, leaving 7a + 4b − 4.
Terms like xy and x are different. In 3xy + 2x − xy + 5x, you get 2xy + 7x. The combine like terms calculator on this site works with one variable at a time, so do multi-variable expressions like these by hand.
Why does combining like terms matter when solving equations?
Most equations become short once you combine like terms on each side. It’s usually the first thing you do before moving anything across the equals sign.
Take 3x + 2 − x = 10. The left side has two x terms, so combine them first: 3x − x = 2x. Now the equation is 2x + 2 = 10. Subtract 2 to get 2x = 8, then divide by 2, and x = 4.
Longer equations follow the same pattern. In 5(x − 2) + 3 = 2x + 8, distributing and combining gives 5x − 7 = 2x + 8, and from there x = 5. The guide on solving linear equations step by step picks up from this point.
What are the most common mistakes?
The main ones are combining unlike terms, dropping a negative sign, and distributing to only the first term in a bracket.
Combining unlike terms usually looks like 2x + 3 = 5x or x + x² = x³. Both are wrong, because the pieces aren’t the same kind of thing. A dropped sign often happens in the middle of a long expression, which is why marking each term with its sign helps. With brackets, check that the number outside reached every term inside.
To check your work, pick a number for x, like 2, and evaluate both the original and your simplified version. For 2(3x − 4) − (x − 5) at x = 2, you get 2(2) − (−3) = 7. For 5x − 3 at x = 2, you get 7. Same value, so the simplification holds. One matching number doesn’t prove it, but a mismatch proves something is wrong.
Frequently asked questions
Why can’t you combine x and x²?
They count different things. x² is x times x, while x is a single x, so adding them doesn’t produce a neater single term. 3x² + 2x stays as two terms.
What does combining like terms mean?
It means adding or subtracting terms that have the same variable and exponent, so the expression has fewer terms. For example, 4x + 2x − 3 becomes 6x − 3.
Are 3x and 3x² like terms?
No. Their variables match but their powers don’t, so they can’t be combined. 3x + 3x² stays as it is.
Can you combine a number with a variable, like 2x + 7?
No. A constant and a variable term aren’t like terms, so 2x + 7 is already simplified.
Is simplifying an expression the same as solving it?
No. An expression has no equals sign, so there’s nothing to solve for. Simplifying rewrites it in a shorter, equivalent form. Solving applies to equations.
What is the coefficient of x when no number is shown?
It’s 1. So x + 4x = 5x, and −x + 4x = 3x.
What order should the simplified answer be in?
The usual convention is descending powers of x with the constant last, such as 2x² + 4x − 6. Other orders are still equal, but this one is easiest to read and compare.