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Home > Maths II > Algebra > Removing brackets

Maths II

Removing brackets

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Baffled by brackets and alarmed by Algebra? Don't be! Go through this revision guide slowly and carefully and you'll soon be able to pass the test.

Multiplying out brackets

If you'd like to refresh your knowledge of basic algebra go to the Manipulations revision bite.

When we multiply out a pair of brackets, everything in the first bracket has to be multiplied by everything in the second bracket.

Example

Multiply out the following equation, and simplify your answer:

(2x + 5) (3x - 4)

This usually means you get four terms in the answer. You might be able to simplify your answer to get only three terms.

There are different ways of seeing where the answer comes from. But one good way is taking each term in the first bracket in turn.

  • Write down the expression carefully -

    (2x + 5)(3x - 4) = 2x(3x - 4) + 5(3x - 4)

  • Multiply out each of the brackets on the right of the expression.

    {2x(3x - 4)} + {5(3x - 4)}

    = {6x^2} - 8x + 15x - 20

  • Collect like terms:

    {6x^2} - 8x + 15x - 20

    = {6x^2} + 7x - 20

Do you see where everything comes from in the second step?

The brackets can be confusing.

Everything inside a bracket is multiplied by everything else.

  • 2x(3x - 4) + 5(3x - 4)

  • 2x \times 3x = {6x^2}

  • 2x (\times -4) = {-8x}

  • 5 \times 3x = 15x

  • 5 (\times -4) = -20

If you still aren't sure about all this, go back to Standard Grade Bitesize Maths I at General level and look at the Revision Bite on Simplifying algebraic terms and simple factorisation

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