Combining like terms | Year 8

01 / LEARN

The idea, step by step

Which terms belong together?

A term is a number, a variable, or a product of numbers and variables. In $5 x + 3 y - 2$ , the terms are $5 x$ , $3 y$ and $- 2$ . Like terms have exactly the same variable part. Thus $5 x$ and $- 2 x$ are like terms, but $5 x$ and $5 y$ are not.

A coefficient counts copies of a variable part. Three copies of $x$ plus four copies of $x$ gives $7 x$ , not $7 x^{2}$ . Constants are collected with other constants.

Keep the sign with the term

Before collecting, attach the sign to each term. In $6 a - 4 + 2 a + 7$ , the constant terms are $- 4$ and $+ 7$ . Grouping does not change these signs. Underlining each family of like terms helps prevent a lost negative sign.

A simplified expression has one term for each variable part. A zero coefficient removes a term. Write $x$ rather than $1 x$ . Simplifying must preserve the value for every allowed input, rather than just one selected number.

A common trap

Writing $3 x + 4 x = 7 x^{2}$ .

Instead: Addition counts copies of $x$ ; it does not multiply the variable factors. The correct result is $7 x$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Collect variables and constants

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

Collect $4 a + 2 a = 6 a$ .
Collect $3 - 5 = - 2$ .
The variable term and constant remain separate.

6 a - 2

Example 2

Two item types

Simplify the cost expression $2 p + 3 q + p - q$ , in dollars.

Collect the $p$ terms: $2 p + p = 3 p$ .
Collect the $q$ terms: $3 q - q = 2 q$ .
Different variable parts cannot combine further.

3 p + 2 q

dollars

Check your understanding

Simplify $8 m - 3 + 2 m + 5$ .

Show answer

$10 m + 2$

$8 m + 2 m = 10 m$ and $- 3 + 5 = 2$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Simplify $6 x + 2 x$ .
2 marks
Simplify $9 a - 4 a$ .
2 marks
Simplify $3 p + 7 + 2 p - 4$ .
2 marks
Simplify $5 x + 2 y - 3 x + y$ .
2 marks
Simplify $4 t - 6 t + 9 - 2$ .
2 marks
Sam says $2 a + 3 b = 5 a b$ . Explain the error.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Simplify $6 x + 2 x$ .
2 marks
Add coefficients: $6 + 2 = 8$ .
$8 x$
Simplify $9 a - 4 a$ .
2 marks
Subtract coefficients: $9 - 4 = 5$ .
$5 a$
Simplify $3 p + 7 + 2 p - 4$ .
2 marks
$3 p + 2 p = 5 p$ and $7 - 4 = 3$ .
$5 p + 3$
Simplify $5 x + 2 y - 3 x + y$ .
2 marks
The $x$ coefficients give $5 - 3 = 2$ .
The $y$ coefficients give $2 + 1 = 3$ .
$2 x + 3 y$
Simplify $4 t - 6 t + 9 - 2$ .
2 marks
$4 - 6 = - 2$ and $9 - 2 = 7$ .
$- 2 t + 7$
Sam says $2 a + 3 b = 5 a b$ . Explain the error.
3 marks
The variable parts $a$ and $b$ differ.
With $a = 1, b = 2$ , the original is $8$ but $5 a b = 10$ .
Unlike terms cannot be collected; the expression remains $2 a + 3 b$ .

Checking saved progress…

Continue learning

Substitution with signed/rational values

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 Mathematics with SA curriculum context

Combining like terms; substitution with signed/rational values; multiplying/dividing algebraic terms; expanding a single bracket; factorising common factors; equivalent linear expressions; rearranging simple formulas.

Official curriculum source ↗

Back to Algebraic expressions