Simplifying algebraic expressions | Year 9

01 / LEARN

The idea, step by step

Only like terms can be collected

A term is a part separated by addition or subtraction. In $5 x - 2 y + 3$ , the terms are $5 x$ , $- 2 y$ and 3. Terms are alike only when their variable parts, including exponents, match.

$5 x + 2 x = 7 x$ counts seven copies of $x$ . But $5 x + 2 y$ cannot be collected without a relationship between $x$ and $y$ . Constants collect with constants. Keep a term attached to its sign when changing its position.

Multiplication is different from collection

$3 x \times 4 x = 12 x^{2}$ : multiply coefficients, then use the index law. This is different from $3 x + 4 x = 7 x$ . Read the operation before deciding what to do.

In a quotient, cancel factors rather than terms. For example, $\frac{8 x^{3}}{2 x} = 4 x^{2}$ for $x \neq 0$ . Keep restrictions from the original denominator, even if a variable disappears after cancellation.

A common trap

Collecting $x$ with $x^{2}$ .

Instead: The variable letters and their exponents must match; $2 x + 3 x^{2}$ remains two terms.

02 / WORKED EXAMPLES

See the thinking

Example 1

Collect terms with signs

Simplify $7 x - 3 y - 2 x + 5 y - 4$ .

Group signed like terms: $(7 x - 2 x) + (- 3 y + 5 y) - 4$ .
$7 x - 2 x = 5 x$ and $- 3 y + 5 y = 2 y$ .
The result is $5 x + 2 y - 4$ .

5 x + 2 y - 4

Example 2

Simplify a product and quotient

Simplify $\frac{6 a^{2} b \times 2 a b}{3 a}$ for $a \neq 0$ .

The numerator becomes $12 a^{3} b^{2}$ .
Divide coefficients and powers: $12 \div 3 = 4$ and $a^{3 - 1} = a^{2}$ .
The result is $4 a^{2} b^{2}$ , still with $a \neq 0$ .

4 a^{2} b^{2}

Check your understanding

Simplify $4 p - 3 q + 2 p + q$ .

Show answer

$6 p - 2 q$

$4 p + 2 p = 6 p$ and $- 3 q + q = - 2 q$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Simplify $3 x + 8 x$ .
1 mark
Simplify $9 a - 4 + 2 a + 7$ .
2 marks
Simplify $5 m - 2 n - 8 m + 6 n$ .
2 marks
Simplify $4 x^{2} + 3 x - 2 x^{2} + 5 x$ .
2 marks
Simplify $3 p^{2} \times (- 2 p)$ .
2 marks
Simplify $\frac{18 x^{3} y}{6 x y}$ for $x, y \neq 0$ .
3 marks

Read the worked solutions

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

Simplify $3 x + 8 x$ .
1 mark
$(3 + 8) x = 11 x$ .
$11 x$
Simplify $9 a - 4 + 2 a + 7$ .
2 marks
$9 a + 2 a = 11 a$ and $- 4 + 7 = 3$ .
$11 a + 3$
Simplify $5 m - 2 n - 8 m + 6 n$ .
2 marks
$5 m - 8 m = - 3 m$ ; $- 2 n + 6 n = 4 n$ .
$- 3 m + 4 n$
Simplify $4 x^{2} + 3 x - 2 x^{2} + 5 x$ .
2 marks
Collect squares separately from first powers: $(4 - 2) x^{2} + (3 + 5) x$ .
$2 x^{2} + 8 x$
Simplify $3 p^{2} \times (- 2 p)$ .
2 marks
$3 (- 2) = - 6$ and $p^{2} p = p^{3}$ .
$- 6 p^{3}$
Simplify $\frac{18 x^{3} y}{6 x y}$ for $x, y \neq 0$ .
3 marks
$18 \div 6 = 3$ , $x^{3 - 1} = x^{2}$ , $y / y = 1$ .
The original denominator excludes zero for either variable.
$3 x^{2}$

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Year 9 algebraic simplification and equivalent expressions, with consolidation of linear formula skills. Binomial expansion and quadratic factorisation/equations are in the separate Quadratics and Parabolas chapter.

Official curriculum source ↗

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