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2.5 Expanding Brackets

GCSE Maths Foundation · Edexcel · Chapter 2: Expressions

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: multiplying out single brackets, expanding and simplifying, and expanding two brackets. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Expand a single bracket, including with a negative number or a letter outside
  • Expand and simplify expressions with two or more brackets
  • Expand the product of two brackets such as (x + 3)(x + 5)
  • Use expanding to write expressions for areas and to show that two expressions are equal

Key words

  • Expand: Multiply out the brackets: 3(x + 4) = 3x + 12.
  • Simplify: Collect like terms after expanding.
  • Binomial: An expression with two terms, such as x + 5.
  • Identity: A statement true for every value of the letter, e.g. 3(x + 4) ≡ 3x + 12.

Expanding a single bracket

Multiply every term inside the bracket by the term outside. An area diagram shows why.

Worked example: single brackets

(a) 5(2a − 3) = 10a − 15
(b) −2(x − 6) = −2x + 12 (−2 × −6 = +12)
(c) x(x + 7) = x² + 7x (d) 2y(3y − 4) = 6y² − 8y

Answer: 10a − 15, −2x + 12, x² + 7x, 6y² − 8y

Careful: A negative number outside the bracket changes the sign of every term inside.

Expand and simplify

Expand each bracket separately, then collect like terms.

Worked example: two brackets added

3(x + 2) + 2(x − 5) = 3x + 6 + 2x − 10
= 5x − 4

Answer: 5x − 4

Worked example: subtracting a bracket

4(2a + 1) − 3(a − 2) = 8a + 4 − 3a + 6
Note −3 × −2 = +6. Collect: 8a − 3a = 5a and 4 + 6 = 10

Answer: 5a + 10

Expanding two brackets

Every term in the first bracket multiplies every term in the second. A grid keeps track of the four products.

Worked example: with negatives

Expand (x − 4)(x + 2)
x × x = x², x × 2 = 2x, −4 × x = −4x, −4 × 2 = −8
x² + 2x − 4x − 8

Answer: x² − 2x − 8

Worked example: squaring a bracket

Expand (x + 3)²
(x + 3)² = (x + 3)(x + 3) = x² + 3x + 3x + 9

Answer: x² + 6x + 9

Common mistakes

  • Only multiplying the first term: 5(2a − 3) is 10a − 15, not 10a − 3.
  • Sign errors with a negative outside: −2(x − 6) is −2x + 12, not −2x − 12.
  • Writing (x + 3)² = x² + 9. You must multiply out (x + 3)(x + 3) to get the middle terms.
  • Forgetting to collect the two middle terms when expanding two brackets.

Revision questions

Try these, then check your answers below each one.

Question 1. Expand 5(x - 3). (Choose from: 5x - 15, 5x - 3, 5x + 15, x - 15.)

Answer: 5x - 15

Working: 5 × x = 5x and 5 × (-3) = -15.

Question 2. Expand x(x + 9). (Choose from: x² + 9x, x² + 9, 2x + 9x, 10x.)

Answer: x² + 9x

Working: x × x = x² and x × 9 = 9x, so x² + 9x.

Question 3. Max says -4(y - 2) = -4y - 8. Is Max correct?

Answer: No

Working: -4 × y = -4y and -4 × (-2) = +8, so -4y + 8. Max is not correct.

Related lessons

Continue in the full course

This lesson is section 2.5 (EGCMF0205) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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