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`