Expanding Brackets

Expanding brackets infographic

What you will learn

• What expanding a bracket means.
• How to expand a single bracket such as 4(x + 3).
• How to expand when the multiplier is negative or a whole bracket is being subtracted.
• How to collect like terms after expanding.
• How to expand two brackets using a grid or a systematic list.
• How to check an expansion by substitution.

Key facts before you start

Why this matters

Brackets are used to keep expressions compact. Expanding them lets you compare expressions, solve equations and move into factorising.

In exams, a correct expansion line often earns method marks even if the problem has more steps afterwards.

Prior knowledge

You should already be comfortable with:

• multiplying positive and negative numbers,
• knowing that 5x means 5 × x,
• collecting like terms,
• using powers such as x²,
• substituting a simple value into an expression.

Clear explanation

What expanding means

To expand a bracket, multiply the term outside the bracket by every term inside the bracket.

The 3 multiplies both terms inside the bracket. It is not enough to multiply only the first term.

Brackets with subtraction

Keep the sign with each term inside the bracket. In 5(y − 2), the second term is −2.

Negative multipliers

A negative term outside the bracket changes signs when it multiplies positive and negative terms.

Expand, then simplify

Some questions have terms outside the bracket too. Expand first, then collect like terms.

Expanding two brackets

For two brackets, multiply each term in the first bracket by each term in the second bracket. A grid can help make sure no product is missed.

Checking by substitution

The expanded expression should have the same value as the bracketed expression. Try an easy value to check.

Worked examples

Quick checks

Choose an answer, then check your thinking.

Practice questions

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For expanding brackets, marks usually come from multiplying every term in the bracket, carrying signs carefully, showing the products for two brackets, and collecting like terms only after the expansion is complete. In area or formula questions, write the expression being expanded before simplifying so the algebra still matches the context.

Common mistakes

• Only multiplying the first term: 3(x + 4) is 3x + 12, not 3x + 4.
• Losing a negative sign: 5(x − 2) gives 5x − 10.
• Changing signs incorrectly: −2(x − 6) gives −2x + 12.
• Missing a product in two brackets: four products are needed before collecting like terms.
• Collecting unlike terms: x² and x are different types of term.

Extension challenge

Expand and simplify (2x − 3)(x + 5).

Exam-board guidance

Expanding brackets questions test whether every term has been multiplied, signs have been controlled and any later simplification is done only after the expansion line is complete.

Next lesson

Next, move into Factorising Expressions.