Expanding Double Brackets
Expanding double brackets means multiplying two brackets together, for example (x + 3)(x + 5), using the fact that every term in the first bracket must multiply every term in the second bracket. This produces four products, often remembered using FOIL (First, Outer, Inner, Last), which are then simplified by collecting the two like middle terms into a quadratic expression.
Method
- Multiply the FIRST term in each bracket together.
- Multiply the OUTER terms: the first term of the first bracket by the second term of the second bracket.
- Multiply the INNER terms: the second term of the first bracket by the first term of the second bracket.
- Multiply the LAST term in each bracket together.
- Write out all four products, keeping careful track of signs whenever a bracket contains a subtraction.
- Collect the two middle (like) terms together to write the answer as a simplified quadratic expression, usually in the order x^2 term, x term, then constant.
Worked example
Expand and simplify (x + 4)(x - 3).
- Multiply the First terms: x x x = x^2.
- Multiply the Outer terms: x x -3 = -3x.
- Multiply the Inner terms: 4 x x = 4x.
- Multiply the Last terms: 4 x -3 = -12.
- Combine all four products: x^2 - 3x + 4x - 12.
- Collect the like x terms: -3x + 4x = x, giving the final answer x^2 + x - 12.
Practice questions
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Q1Expand and simplify (x + 2)(x + 5).Show answer
Answer: x^2 + 7x + 10
Q2Expand and simplify (x + 6)(x - 2).Show answer
Answer: x^2 + 4x - 12
Q3Expand and simplify (x - 3)(x - 4).Show answer
Answer: x^2 - 7x + 12
Q4Expand and simplify (x - 5)(x + 5).Show answer
Answer: x^2 - 25
Q5Expand and simplify (2x + 1)(x + 3).Show answer
Answer: 2x^2 + 7x + 3
Q6Expand and simplify (x + 7)^2.Show answer
Answer: x^2 + 14x + 49
Q7Expand and simplify (3x - 2)(x - 4).Show answer
Answer: 3x^2 - 14x + 8
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Expand and simplify (x + 8)(x - 5).
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Expand and simplify (2x - 3)(x + 4).
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Show that (x + 6)^2 = x^2 + 12x + 36, and explain why (x + 6)^2 is NOT equal to x^2 + 36.
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Free printable worksheet
Want more practice on paper? Download the expanding double brackets worksheet pack - 8 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 28 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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