How Do You Combine Like Terms in an Algebraic Expression?

To combine like terms, add or subtract the coefficients of terms that have exactly the same variable part and leave that variable part unchanged. For example, (5x + 3x = 8x), but (5x + 3y) cannot be combined because (x) and (y) are different variables. This works for any polynomial expression, with one extra step: if parentheses are present, distribute first, then combine.

What Counts as a "Like Term"

Two terms are like terms only when their variable parts match completely — same variables, same exponents. The coefficients do not need to match; in fact, they are the numbers you combine.

A useful habit: rewrite each term so variables appear in alphabetical order ((2yx \to 2xy)) before deciding whether terms match.

The Core Procedure

1. Scan the expression and mark terms with identical variable parts.
2. Keep the sign in front of each term. In (8x - 3x + 2x), the terms are (8x), (-3x), and (2x).
3. Add the coefficients of each group: (8 - 3 + 2 = 7), so the (x)-terms become (7x).
4. Write the simplified expression with the combined terms and any terms that had no partner.

Worked example:

[ 9m + 4 - 2m + 7 ]

• (m)-terms: (9m - 2m = 7m)
• Constants: (4 + 7 = 11)
• Result: (7m + 11)

Handling Negative Signs and Subtraction

Most errors come from dropping a minus sign. Treat subtraction as adding a negative term, and move the sign with the term when you regroup:

[ -6k + 10 - k - 15 = (-6k - k) + (10 - 15) = -7k - 5 ]

If a term has no visible coefficient, it is (1): (-k) means (-1k), and (x) means (1x).

When Parentheses Are Involved: Distribute First

You cannot combine terms across a set of parentheses until the parentheses are removed. Apply the distributive property, then combine.

[ 3(2x + 5) - 4(x - 1) ]

1. Distribute: (6x + 15 - 4x + 4) (note: (-4 \times -1 = +4))
2. Combine: ((6x - 4x) + (15 + 4) = 2x + 19)

Watch the sign on the second distribution — a negative multiplier flips the sign of every term inside the parentheses.

Verify Your Answer

Substitute a simple number for the variable in both the original and simplified expressions; the values should match.

Using (x = 2) in the example above:

• Original: (3(4 + 5) - 4(2 - 1) = 27 - 4 = 23)
• Simplified: (2(2) + 19 = 23)

A match does not prove the simplification is correct for every value, but a mismatch reliably signals an error — usually a sign or a distribution mistake.

Common Pitfalls

• Combining unlike terms. (3x^2 + 4x) stays as is; it does not become (7x^2) or (7x).
• Changing the exponent. Combining (2x^3 + 5x^3) gives (7x^3), not (7x^6). Exponents are never added when combining terms.
• Losing signs during regrouping. Keep each sign attached to its term, especially when moving terms around.
• Skipping distribution. Parentheses must be cleared before any combining happens.

Where to Practice

Algebra House (algebrahouse.com) offers algebra examples, answered questions, and state test and ACT/SAT practice sections, which is a reasonable place to find additional worked problems and check your steps against a full solution.