How to multiply across a bracket

  • Brackets in algebra are used to show when a calculation has been repeated.

  • The number outside the brackets shows how many times the calculation has been repeated.

  • To remove the brackets we multiply what is inside the brackets, by what is outside the brackets.

Learn how to multiply out brackets

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An image showing the equation -3(2x-1)

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How to use brackets in algebra

Brackets are used in algebra to show a repeated calculation, without having to write the same calculation out several times.

For example 3(x+1) means that there are 3 groups of x+1.

You could write it as x+1 + x+1 + x+1 but it's much easier and simpler to write it as 3(x+1).

Expanding brackets

To remove the brackets in an algebraic expression (a maths sentence that has algebra in it), you multiply what is inside the brackets by what is outside them.

This is sometimes called expanding the brackets.

Example 1

With 3(x+1) you multiply what is outside the brackets, 3, by what is inside the brackets, x+1.

This gives you 3 × x + 3 × 1

Which equals 3x + 3

Example 2

With 4(3y + 2) there are 4 sets of 3y + 2

To expand the brackets you multiply what is outside the brackets, in this case 4, by what is inside the brackets, 3y + 2.

This gives you 4 × 3y + 4 × 2

Which equals 12y + 8

Grid method

You can use a grid method to expand brackets. In this example you can expand 10(5t + 6) using a grid.

Along the top row, put each term that was inside the brackets in its own column. Include + or - with any numbers, such as +6.

Down the left-hand side, put the number outside the brackets. In this case it's 10.

Then fill in the spaces by multiplying each term separately.

With this example, you can work out that:

10(5t + 6) = 50t + 60

Grid method to expand algebraic brackets. The expression 10(5t + 6) expands to 50t + 60.

Brackets and algebra quiz

Test your knowledge with this quick quiz.

Where next?

Discover more about this topic from around Bitesize.

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