Expanding Single Brackets
Expanding a single bracket means multiplying every term inside the bracket by the term directly outside it, using the distributive law a(b + c) = ab + ac. This applies whenever a number or letter sits immediately next to a bracket, and it is essential whenever the term outside is negative, since multiplying by a negative flips the sign of every term inside the bracket.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify the term directly outside the bracket, including its sign.
- Multiply the outside term by the FIRST term inside the bracket.
- Multiply the outside term by the SECOND (and any further) term inside the bracket, keeping careful track of signs.
- Write the products in a row with the correct + or - sign between them.
- If the term outside the bracket is negative, remember that multiplying by a negative flips the sign of every term inside the bracket.
- Collect any like terms after expanding, if the expression contains more than one bracket or extra terms.
Worked example
Expand and simplify 5(2x + 3) - 3(x - 4).
- Expand the first bracket: 5(2x + 3) = 5 x 2x + 5 x 3 = 10x + 15.
- Expand the second bracket: -3(x - 4) = -3 x x + (-3) x (-4) = -3x + 12.
- Write the full expression: 10x + 15 - 3x + 12.
- Collect like terms: 10x - 3x = 7x, and 15 + 12 = 27.
- Final answer: 7x + 27.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Expand 3(x + 5).Show answer
Answer: 3x + 15
Q2Expand 4(2x - 1).Show answer
Answer: 8x - 4
Q3Expand -2(x + 6).Show answer
Answer: -2x - 12
Q4Expand and simplify 2(x + 3) + 3(x + 1).Show answer
Answer: 5x + 9
Q5Expand and simplify 6(x - 2) - 2(x - 5).Show answer
Answer: 4x - 2
Q6Expand -3(2x - 4).Show answer
Answer: -6x + 12
Q7Expand and simplify 4(3x + 2) - 5x.Show answer
Answer: 7x + 8
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Expand and simplify 7(x + 2) - 3(x - 1).
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A student says that -4(x - 5) expands to -4x - 20. Show that the student is wrong, and give the correct expansion.
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Free printable worksheet
Want more practice on paper? Download the expanding single brackets worksheet pack - 5 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 23 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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