Year 7 - Expressions and the distributive law - Free practice

Year 7 Expressions and the Distributive Law Worksheets & Practice

Expand, simplify and build algebraic expressions. Worked solutions every time, free.

Quick answer

How do you expand brackets using the distributive law?

Multiply the term outside the bracket by every term inside it. For example, 3(x + 4) = 3×x + 3×4 = 3x + 12. If the term outside is negative, every sign inside flips: −2(x + 5) = −2x − 10. After expanding, collect any like terms to simplify fully.

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Worked examples

Year 7 expressions and the distributive law: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Expanding brackets using the distributive law
Expand $3(x + 5)$ .
Show worked solution
Key idea: The distributive law says $a(b + c) = ab + ac$ . Multiply the term outside the brackets by every term inside.
1. Multiply $3$ by $x$ : $3 \times x = 3x$
2. Multiply $3$ by $5$ : $3 \times 5 = 15$
3. Write the expanded expression: $3x + 15$
Answer: $3x + 15$
Example 2 · Expanding and simplifying with a negative term outside brackets
Expand and simplify $4(2x + 3) - 2(x - 1)$ .
Show worked solution
Key idea: Expand each bracket separately using the distributive law, taking care with the negative sign, then collect like terms.
1. Expand $4(2x + 3)$ : $4 \times 2x + 4 \times 3 = 8x + 12$
2. Expand $-2(x - 1)$ : $-2 \times x + (-2) \times (-1) = -2x + 2$
3. Write the full expression: $8x + 12 - 2x + 2$
4. Collect like terms: $(8x - 2x) + (12 + 2) = 6x + 14$
Answer: $6x + 14$
Example 3 · Writing and expanding an expression from a real-world problem
A school canteen sells pies for $3 each and drinks for $2 each. A teacher buys the same combination of 4 pies and 3 drinks for each of 5 classes. Write an expression for the total cost, then calculate it.
Show worked solution
Key idea: Write the cost for one class as a bracketed expression, multiply by the number of classes, then expand and evaluate.
1. Cost for one class: $(4 \times 3 + 3 \times 2)$ dollars $= (12 + 6)$ dollars. Written generally as a bracketed expression before calculating: $5(4 \times 3 + 3 \times 2)$
2. Expand using the distributive law: $5 \times 12 + 5 \times 6$
3. Calculate each part: $60 + 30$
4. Total cost: $90$
Answer: The total cost is $90.

Common mistakes

Where students usually lose marks

Only multiplying the first term inside the brackets

$3(x + 5) = 3x + 5$

The distributive law requires you to multiply the outside term by every term inside the brackets. Both $x$ and $5$ must be multiplied by $3$ , giving $3x + 15$ .

Ignoring the negative sign when expanding

$-2(x - 1) = -2x - 2$

Multiply the negative sign through to every term inside: $-2 \times (-1) = +2$ , so the result is $-2x + 2$ . Write out the multiplication for each term separately to avoid sign errors.

Adding unlike terms when collecting like terms

$3x + 5 = 8x$

Only like terms (same variable and power) can be added or subtracted. $3x$ and $5$ are unlike terms, so $3x + 5$ cannot be simplified further.

Confusing the commutative and distributive laws

$3(x + 5) = (3 + x)(3 + 5)$

The commutative law swaps the order of terms in addition or multiplication ( $a + b = b + a$ ). The distributive law expands a bracket by multiplying: $3(x + 5) = 3x + 15$ . Keep these two laws separate in your mind.

Try one yourself

Your turn

Expand and simplify: $4(2x + 3) + 5x$

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About this worksheet

Why we built it

The distributive law is one of the most important building blocks in Year 7 algebra. It explains why a(b + c) = ab + ac, and it connects the arithmetic your student already knows to the world of algebraic expressions. These worksheets guide students from writing simple expressions all the way to expanding and simplifying brackets, with full worked solutions so every mistake can be traced and fixed.

What's covered

Sub-skills your student will practise

✓Writing algebraic expressions from word descriptions
✓Applying the commutative and associative laws
✓Expanding single brackets using the distributive law
✓Expanding expressions with negative terms outside brackets
✓Simplifying expanded expressions by collecting like terms
✓Translating real-world problems into algebraic expressions

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Frequently asked

Questions parents ask about expressions and the distributive law

What does the distributive law actually mean in Year 7 maths?

The distributive law says you can multiply a term outside a bracket by every term inside it. For example, 3(x + 4) becomes 3x + 12. It works for numbers too, so 6 × 23 can be calculated as 6 × 20 + 6 × 3.

What is the difference between an expression and an equation at this level?

An expression is a maths phrase with no equals sign, such as 2x + 5. An equation sets two expressions equal to each other, like 2x + 5 = 11. Year 7 students learn to write and simplify expressions before they start solving equations.

Why do students lose marks when expanding brackets?

The most common mistake is only multiplying the first term inside the bracket, forgetting the second. Another frequent error is dropping a negative sign when the term outside the bracket is negative. Worked solutions help students spot exactly where their working goes wrong.

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