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Auralith Learning

Year 8 · Maths · Brackets and equations · Lesson 1

Expanding brackets

Learn what a bracket means and how to expand single brackets using a grid, including negative numbers and x outside the bracket, then expand and simplify.

Whiteboard video lesson: Expanding brackets

30-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Understand what a number outside a bracket means
  • Expand a single bracket using the grid method
  • Expand brackets with negative numbers
  • Expand brackets with a letter outside
  • Expand and simplify expressions

The method

  1. Multiply the outside term by every term inside the bracket.
  2. Keep the sign with each term.
  3. Negative × negative = positive; negative × positive = negative.
  4. Collect like terms.

Key words: expand, bracket, term, like terms, simplify.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Expand 3(x + 4).

  1. Step 1: Draw a grid
  2. Step 2: Multiply by x
  3. Step 3: Multiply by 4
  4. Step 4: 3(x + 4) = 3x + 12

Answer: 3x + 12

Question 2

Expand 6(x + 1).

  1. Step 1: Draw a grid
  2. Step 2: Multiply by x
  3. Step 3: Multiply by 1
  4. Step 4: 6(x + 1) = 6x + 6

Answer: 6x + 6

Question 3

Expand 4(x − 5).

  1. Step 1: Draw a grid
  2. Step 2: Multiply by x
  3. Step 3: Multiply by −5
  4. Step 4: 4(x − 5) = 4x − 20

Answer: 4x − 20