Expanding Double Brackets
(KS3, Year 8)
Double brackets are two brackets written next to each other. The two brackets are multiplying each other.

expand double brackets explained Expanding double brackets means multiplying terms in the pair of expressions to remove the brackets. Imagine we wanted to remove the brackets from the pair of expressions below. We have to expand the brackets. expand_double_brackets

How to Expand Double Brackets

Expanding double brackets is easy.

Question

Expand the double brackets below.
expand double brackets example

Step-by-Step:

1

Write the first term in the first brackets (x) in front of the second brackets (x + 2). expand_double_brackets_step_1
x(x + 2)

2

Write the second term in the first brackets (1) in front of the second brackets (x + 2), and add to the previous result. expand_double_brackets_step_2
x(x + 2) + 1(x + 2)
Note: The term is added because there is a + before the second term in the first brackets.
We have written the double brackets as single brackets added together.

3

Expand the first single brackets, x(x + 2).
  • Multiply the first term inside the brackets (x) with the term outside the brackets (x). expand_double_brackets_step_3_1
    x × x = x2 x2
  • Multiply the second term inside the brackets (2) with the term outside the brackets (x), and add to the previous result expand_double_brackets_step_3_2
    x × 2 = 2x x2 + 2x
We have expanded the first single brackets
x(x + 2) = x2 + 2x

4

Expand the second single brackets, 1(x + 2).
  • Multiply the first term inside the brackets (x) with the term outside the brackets (1). expand_double_brackets_step_4_1

    1 × x = x

    x

  • Multiply the second term inside the brackets (2) with the term outside the brackets (1), and add to the previous result. expand_double_brackets_step_4_2

    1 × 2 = 2

    x + 2

We have expanded the second single brackets
1(x + 2) = x + 2
We have expanded all brackets.

5

Replace the single brackets with their expansions.

expand double brackets step 5

6

Simplify the expression if necessary by collecting like terms together. In our example, we can collect the x terms together.
x2 + 2x + x + 2 = x2 + 3x + 2

Answer:

We have expanded the double brackets. expand_double_brackets_answer

Lesson Slides

The slider below shows another real example of how to expand double brackets.

Multiplication Tips

  • Multiplying a number with a variable

    2 × x = 2x

    5 × x = 5x

  • Multiplying a number with a variable with a coefficient

    2 × 2x = 4x

    3 × 5x = 15x

  • Multiplying a variable with a variable

    x × y = xy

    x × x = x2

Beware

Be Careful with Signs

Each term in the brackets will have a sign. x plus 2 minus y
  • positive terms have a + sign in front of them, or no sign if it is the first term.
  • negative terms have a − sign in front of them.
These signs must be included when multiplying terms. positive times positive and positive times negative Remember the rules for multiplying different signs: Same signs give a plus: plus times plus equals plus. minus times minus equals plus Different signs give a minus: plus times minus equals minus. minus times plus equals minus
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This page was written by Stephen Clarke.