Free worksheet · Australian Curriculum

Collecting like terms worksheets with answers

Collecting like terms is how you simplify an algebraic expression. Learn what makes terms alike and how to handle the signs, then practise with fresh questions and worked solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Collecting like terms, explained

What counts as a like term, and the sign rule that most mistakes come from.

1. What like terms are

Like terms have exactly the same letters, raised to the same powers. Only the number in front can differ.

$5a$ and $3a$ are like terms.
$4x$ and $4y$ are not.
$3x^2$ and $3x$ are not, because the powers differ.

2. Add or subtract the numbers in front

Keep the letters the same and combine the numbers:

$5a + 3a = 8a 9y - 3y = 6y$

3. The sign belongs to the term after it

Each term carries the sign in front of it. Group like terms with their signs:

$4m - 9 - m + 2 = (4m - m) + (-9 + 2) = 3m - 7$

A letter on its own, like $m$ , means $1m$ .

4. More than one letter

Collect each kind separately:

$7x - 2y + 3x + 5y = 10x + 3y$

The answer has two terms because $x$ and $y$ terms can't be combined.

5. Order of letters doesn't matter

$ab$ and $ba$ are the same, because multiplication can be done in any order. So

$2ab + 5ba = 7ab$

6. Terms with powers

Treat $x^2$ terms and $x$ terms as different kinds:

$3x^2 + 2x - x^2 + 5x = 2x^2 + 7x$

Quick check: 10 questions

Try each one, then open the answer.

Simplify $6x + 4x$ .
Answer
$10x$
Simplify $9y - 3y$ .
Answer
$6y$
Simplify $5a + 2b + 3a$ .
Answer
$8a + 2b$
Simplify $4p - 7 + 2p + 3$ .
Answer
$6p - 4$
Simplify $8m - 3n - 5m + n$ .
Answer
$3m - 2n$
Simplify $x + x + x$ .
Answer
$3x$
Simplify $3xy + 4yx$ .
Answer
$7xy$
Simplify $2k^2 + 5k - k^2 + 3k$ .
Answer
$k^2 + 8k$
Simplify $-4a + 6b - 2a - b$ .
Answer
$-6a + 5b$
A rectangle has sides $3x + 2$ and $x - 1$ . Write a simplified expression for its perimeter.
Answer
$2(3x + 2) + 2(x - 1) = 8x + 2$

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetExpressions and the distributive law Year 7 worksheetAlgebra Year 8 worksheetAlgebra Year 9 worksheetAlgebra

Questions

What are like terms?

Like terms have exactly the same letters raised to the same powers, such as 5a and 3a. Only the number in front can be different.

Can you collect x and x squared?

No. x and x squared are different kinds of term, so an expression like 3x squared plus 2x can't be simplified any further.

What is the most common mistake when collecting like terms?

Losing the sign. Each term carries the sign in front of it, so in 4m minus 9 minus m, the m term is negative.

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