Multiplying Terms over Brackets

Multiplying Terms over Brackets

GCSE(F), GCSE(H),

Multiplying out brackets is expanding an expression.

For example: expand 3a(4a - 3b + 6). Set out the terms within the brackets as a list, deal with them individually, then add them together:

4a x 3a = 12a2

-3b x 3a = -9ab

6 x 3a = 18a

Note that every term in the bracket is multiplied by the term outside the bracket, and that negative signs are taken into account. Put the answer together:

3a(4a - 3b + 6) = 12a2 - 9ab + 18a

Examples

1. Expand and simplify 3(m + 2) + 4m.

Answer: 7m + 6

Expand the bracket:

m x 3 = 3m

2 x 3 = 6

Put it all together. Include the 4m that was outside the bracket:

3m + 6 + 4m = 7m + 6

2. Expand and simplify: 6 - a(a - 2).

Answer: -a2 + 2a + 6

Expand the brackets, taking very careful note of the negative signs:

a x -a = -a2

-2 x -a = 2a

Putting it all together, with the leading 6:

-a2 + 2a + 6

It is normal to put a list of terms in descending order of their powers.