Expanding single brackets | Year 9

01 / LEARN

The idea, step by step

Multiply the whole group

$a (b + c) = a b + a c$ counts $a$ copies of each part of a sum. A rectangle of height 3 and width $x + 4$ has area $3 (x + 4) = 3 x + 12$ . The diagram shows both areas inside the same rectangle.

Write each separate multiplication before simplifying. Each term in the bracket must receive the outside multiplier. This makes a missing product or sign easier to notice.

Distribute signs as well as numbers

For $- 2 (3 x - 5)$ , both $3 x$ and $- 5$ are multiplied by $- 2$ . The second product is positive, so the result is $- 6 x + 10$ .

A minus before brackets means multiplication by $- 1$ : $7 - (2 x - 3) = 7 - 2 x + 3 = 10 - 2 x$ . Expand all groups first, then collect like terms. Signs outside the group do not change unless an operation requires it.

A common trap

Only multiplying the first term in a bracket.

Instead: Make one product for each term: $5 (x + 2) = 5 x + 10$ , not $5 x + 2$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Expand and collect

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

Distribute 4: $8 x + 12 - 5 x$ .
Collect $8 x - 5 x = 3 x$ .
The answer is $3 x + 12$ .

3 x + 12

Example 2

Subtract a whole product

Simplify $6 - 3 (2 y - 4)$ .

$3 (2 y - 4) = 6 y - 12$ .
$6 - (6 y - 12) = 6 - 6 y + 12$ .
Collect constants to obtain $18 - 6 y$ .

18 - 6 y

Check your understanding

Expand $- 4 (x - 3)$ .

Show answer

$- 4 x + 12$

$(- 4) x + (- 4) (- 3) = - 4 x + 12$ .

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Expand $3 (x + 7)$ .
2 marks
Expand $5 (2 a - 3)$ .
2 marks
Expand $- 2 (4 p + 1)$ .
2 marks
Simplify $7 - (3 x + 2)$ .
2 marks
Simplify $2 (3 y - 4) + 5 (y + 1)$ .
3 marks
A rectangle is 6 cm high and $(x + 2)$ cm wide. Write its area without brackets.
3 marks

Read the worked solutions

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

Expand $3 (x + 7)$ .
2 marks
$3 x + 3 (7) = 3 x + 21$ .
$3 x + 21$
Expand $5 (2 a - 3)$ .
2 marks
Multiply both terms by 5.
$10 a - 15$
Expand $- 2 (4 p + 1)$ .
2 marks
$(- 2) (4 p) + (- 2) (1) = - 8 p - 2$ .
$- 8 p - 2$
Simplify $7 - (3 x + 2)$ .
2 marks
$7 - 3 x - 2 = 5 - 3 x$ .
$5 - 3 x$
Simplify $2 (3 y - 4) + 5 (y + 1)$ .
3 marks
Expand: $6 y - 8 + 5 y + 5$ .
Collect: $11 y - 3$ .
$11 y - 3$
A rectangle is 6 cm high and $(x + 2)$ cm wide. Write its area without brackets.
3 marks
$A = 6 (x + 2) = 6 x + 12$ cm $2$ .
$6 x + 12$ cm $2$

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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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