A number sitting outside a bracket multiplies everything inside it. To expand the bracket, multiply the outside term by each term in turn and add the results. This is the distributive law, now written with a letter:

It is the same distributive law you already use for numbers — splitting one multiplication into two easy ones — only now one of the terms is an unknown.

A worked example

Take 3(x + 4). Multiply the outside 3 by each term inside — by the x, then by the 4:

We cannot add 3x and 12 together — they are not like terms — so 3x + 12 is the finished, expanded form.

See it as an area

A rectangle 3 tall and x + 4 wide has area 3(x + 4). Slice it along the line between the x part and the 4 part and you get two rectangles: one 3 \times x = 3x and one 3 \times 4 = 12. Nothing moved, so the two areas must add up to the whole. Step through it.

The same trick works when the outside term is itself a letter. Multiply the x by each term inside:

Here x \times x = x^2 (an x times an x), and x \times 2 = 2x. So multiplying a bracket by a letter can raise the power.