Expanding a bracket multiplies what is outside into each term inside. Factorising runs that in reverse: you start with a sum of terms and pull a shared multiplier back out to the front. So expanding turns 3(2x + 3) into 6x + 9; factorising turns 6x + 9 back into 3(2x + 3).

Find what every term shares

Look at each term and ask: what is the largest thing that divides all of them? That is the common factor. For 6x + 9, both 6x and 9 are divisible by 3, so take 3 out:

This is just the distributive law read backwards. Multiply the bracket out again to check: 3 \times 2x = 6x and 3 \times 3 = 9, giving 6x + 9 — back where we started.

The factor can be a letter too

A shared factor need not be a number. In x^2 + x, both terms contain an x (remember x^2 = x \times x), so x comes out:

Watch the hidden 1: when you take a term out completely, what is left inside is 1, not nothing.

See it as an area

Picture 6x + 9 as the area of a rectangle split into two pieces — a 6x part and a 9 part. Both pieces are the same height, and that shared height is the common factor. Read the height off the side, and the two widths along the bottom spell out the bracket. Step through it.

See it explained

Khan Academy factors a sum by pulling out the greatest common factor — the distributive law in reverse: