∑∫ax²+bx+c=0π√x

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By MathPal Editorial Team·PublishedApr 17, 2026

Grade: 7-8 | Topic: Algebra

What You Will Learn

Combining like terms is one of the most fundamental skills in algebra. Every time you simplify an expression or solve an equation, you will use it. In this guide you will learn what makes terms "like," how to identify the coefficient and variable parts of a term, and how to combine terms correctly — even in multi-variable expressions with negative numbers.

Theory

What is a term?

A term is a single piece of an algebraic expression — a number, a variable, or a number multiplied by one or more variables. Terms are separated by + or − signs.

In the expression 4x+7y−3, there are three terms: 4x, 7y, and −3.

Every term has two parts:

• Coefficient — the numerical factor in front of the variable. In 4x, the coefficient is 4. If no number is written, the coefficient is 1 (so x really means 1x). A bare negative sign means −1 (so −x means −1x).
• Variable part — the letter(s) and their exponents. In 4x, the variable part is x.

A term with no variable at all, such as −3, is called a constant term.

What are like terms?

Like terms are terms whose variable parts are identical — the same variables raised to the same powers. Only the coefficients can differ.

How to combine like terms

To combine like terms, add or subtract their coefficients and keep the variable part unchanged:

5x+3x=(5+3)x=8x

9y−4y=(9−4)y=5y

When an expression has several different variable groups, combine each group separately:

2x+5y+3x−y=(2x+3x)+(5y−y)=5x+4y

Working with negative coefficients

Negative signs belong to the term that follows them. Treat subtraction as adding a negative:

7a−10a=(7+(−10))a=−3a

−2m−5m=(−2+(−5))m=−7m

Worked Examples

Example 1 — Simple one-variable expression

Simplify 6x+2x−x.

Step 1: Identify like terms. All three terms contain x.

Step 2: Add the coefficients: 6+2+(−1)=7.

Step 3: Write the result: 7x.

Example 2 — Multi-variable expression

Simplify 3a+4b−2a+b.

Step 1: Group the a-terms and b-terms:

(3a−2a)+(4b+b)

Step 2: Combine each group:

1a+5b=a+5b.

Example 3 — Expression with exponents

Simplify 5x²+3x−2x²+7x+4.

Step 1: Identify the groups:

• x² terms: 5x² and −2x²
• x terms: 3x and 7x
• Constants: 4.

Step 2: Combine each:

(5−2)x²+(3+7)x+4=3x²+10x+4

Example 4 — After the distributive property

Simplify 2(3x+4)+5x−12.

Step 1: Distribute: 6x+8+5x−12.

Step 2: Group: (6x+5x)+(8−12).

Step 3: Combine: 11x−4.

Common Mistakes

Mistake 1 — Combining unlike terms

❌ 3x+4x²=7x²
✅ 3x+4x² — these are NOT like terms (different exponents on x), so the expression is already simplified.

Mistake 2 — Forgetting the coefficient of 1

❌ x+5x=5x
✅ x+5x=1x+5x=6x — remember that x alone has a coefficient of 1.

Mistake 3 — Dropping the negative sign

❌ 8y−3y−2y=7y
✅ 8y−3y−2y=(8−3−2)y=3y — subtract both 3 and 2 from 8.

Practice Problems

Problem 1: Simplify 4m+9m.
Show Answer: 4m+9m=13m.

Problem 2: Simplify 7x−3x+2.
Show Answer: 7x−3x+2=4x+2.

Problem 3: Simplify 2a+3b−a+5b.
Show Answer: (2a−a)+(3b+5b)=a+8b.

Problem 4: Simplify 6x²−x+4x²+3x−5.
Show Answer: (6x²+4x²)+(−x+3x)+(−5)=10x²+2x−5.

Problem 5: Simplify 3(2y−1)+4y+7.
Show Answer: First distribute: 6y−3+4y+7. Then combine: (6y+4y)+(−3+7)=10y+4.

Summary

• Like terms share exactly the same variable(s) raised to the same power(s).
• To combine like terms, add or subtract the coefficients and keep the variable part the same.
• Always watch for hidden coefficients of 1 or −1.
• Group terms by their variable part before combining to stay organized.
• Combining like terms is used constantly in simplifying expressions, solving equations, and working with polynomials.