Free worksheet · Australian Curriculum

Expanding brackets worksheets with answers

Expanding means multiplying out brackets so there are none left. Learn single brackets, negatives and binomial products, then make a free worksheet with full solutions.

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

Topic guide

Expanding brackets, explained

From Year 7 single brackets to the Year 9 and 10 binomial products, step by step.

1. The distributive law

Multiply the term outside by every term inside:

$3(x + 5) = 3x + 15 4(2a - 3) = 8a - 12$

2. A negative outside the bracket

The negative multiplies every term, so every sign inside changes:

$-3(2x - 5) = -6x + 15$

A minus times a minus is a plus. This is where most marks are lost.

3. Expand, then simplify

Expand each bracket, then collect like terms:

$4(x + 2) - 3(x - 1) = 4x + 8 - 3x + 3 = x + 11$

4. A pronumeral outside the bracket

The same law applies, using index laws to multiply:

$x(x + 3) = x^2 + 3x 2a(5a - 4) = 10a^2 - 8a$

5. Binomial products

Multiply every term in the first bracket by every term in the second (some students remember it as FOIL):

$(x + 3)(x + 5) = x^2 + 5x + 3x + 15 = x^2 + 8x + 15$

6. Perfect squares and the difference of two squares

Two patterns are worth knowing:

$(x + 4)^2 = x^2 + 8x + 16 (x - 5)(x + 5) = x^2 - 25$

$(x + 4)^2$ is not $x^2 + 16$ : the middle term $8x$ is easy to forget.

Quick check: 10 questions

Try each one, then open the answer.

Expand $4(x + 3)$ .
Answer
$4x + 12$
Expand $-2(y - 5)$ .
Answer
$-2y + 10$
Expand $a(a + 7)$ .
Answer
$a^2 + 7a$
Expand $3x(2x - 4)$ .
Answer
$6x^2 - 12x$
Expand and simplify $5(x + 2) + 3(x - 1)$ .
Answer
$8x + 7$
Expand and simplify $2(3k + 1) - 4(k - 2)$ .
Answer
$6k + 2 - 4k + 8 = 2k + 10$
Expand $(x + 2)(x + 6)$ .
Answer
$x^2 + 8x + 12$
Expand $(x - 3)(x + 7)$ .
Answer
$x^2 + 4x - 21$
Expand $(2x + 1)(x - 4)$ .
Answer
$2x^2 - 7x - 4$
Expand $(x + 5)^2$ .
Answer
$x^2 + 10x + 25$

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

Questions

What does expanding brackets mean?

Expanding means multiplying out the brackets so the expression has no brackets left. The term outside multiplies every term inside.

What is the most common mistake when expanding?

Forgetting to multiply every term, or forgetting that a negative outside the bracket changes every sign inside. Expanding and checking a few with numbers helps catch these.

When do students learn binomial expansion?

Single brackets come up in Years 7 and 8. Expanding two brackets, such as binomial products and perfect squares, is Year 9 and Year 10 algebra.

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