Collecting Like Terms

What you will learn

• Spot like terms.
• Add and subtract their coefficients.
• Write a fully simplified expression.

Before you start: you should know terms and coefficients and how to add and subtract negative numbers. See Algebraic Expressions.

The idea

Like terms have exactly the same letters raised to the same powers. $5x$ and $-2x$ are like terms. $5x$ and $5x^2$ are not, and neither are $3a$ and $3b$.

The rule

Add or subtract the coefficients and keep the letter part. $3x + 5x = 8x$ because $3$ lots of $x$ plus $5$ lots of $x$ makes $8$ lots of $x$.

Keep the sign with the term

The sign in front of a term belongs to that term. In $6a + 3b - 2a - b$, the terms are $+6a$, $+3b$, $-2a$ and $-b$. Remember that $-b$ means $-1b$.

Worked examples

Example 1: Two letters

Simplify $6a + 3b - 2a - b$.

1. Group: $(6a - 2a) + (3b - b)$.
2. Combine: $4a + 2b$.

Answer: $4a + 2b$

Example 2: With constants

Simplify $5x + 2 - 3x + 4$.

1. Group $x$ terms: $5x - 3x = 2x$.
2. Group constants: $2 + 4 = 6$.

Answer: $2x + 6$

Example 3: Powers

Simplify $3x^2 + 4x - x^2 + 2x$.

1. $x^2$ terms: $3x^2 - x^2 = 2x^2$.
2. $x$ terms: $4x + 2x = 6x$.

Answer: $2x^2 + 6x$

Tip: underline or circle each group of like terms in a different way before combining them.

Why it matters

Collecting like terms makes expressions shorter and easier to use. It is the first step in solving equations and expanding brackets. Next: expanding brackets.