First note that anything just outside of a bracket means “Multiply this by what’s inside the bracket”

e.g. 2(5) = 2x5

      2(y + 5) = 2x(y + 5)

Now let’s try something with numbers:

2(3+7)

BIDMAS says work out the brackets first (work out what's inside the bracket) so we get:

2(10) = 2x10 = 20

A different method: What if we didn’t work out the brackets first? Is there another way we could arrive at the same answer? Well yes, there is. You multiply whatever’s outside the bracket by both parts insides.

So:

2(3 + 7) = 2x3 + 2x7 = 6 + 14 = 20

 

When we do this with algebra, we do exactly the same thing, we just can’t usually get a straightforward number at the end. For example:

2(y + 7) = 2y + 14

A common mistake people make when multiplying out brackets is to just to multiply the number outside by the first term on the inside.

This is WRONG 2(y + 7) = 2y + 7

This is like saying 2(3 + 7) = 6 + 7 = 11

As we saw earlier, this is not true!

So always remeber to multiply everything within the brackets by whatever number is outside of the brackets.

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AQA Unit 2 November 2011 (F) - Page 11, Questioin 15(d)

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