Multiplying Terms over Brackets

## Multiplying Terms over Brackets

Multiplying out brackets is expanding an expression.

For example: expand 3a(4a - 3b + 6). Each term inside the bracket needs to be multiplied by the term, 3a, outside the bracket. Set out the terms within the brackets as a table:

 4a -3b +6 3a 12a^2 -9ab +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) = 12a^2 - 9ab + 18a<

## Example 1

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

Expand the bracket:

3 xx m = 3m

3 xx 2 = 6

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

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

Answer: 7m + 6

## Example 2

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

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

a xx -a = -a^2

-2 xx -a = 2a

Putting it all together, with the leading 6:

-a^2 + 2a + 6

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

Answer: -a^2 + 2a + 6