Ab + 4a - 3b - 12

Step by step

The question

Question: factor ab + 4a − 3b − 12.

There are four terms.

So we factor them in pairs.

This is called grouping.

1 Group in pairs

We put the first two together, and the last two together.

From the first pair we take out a.

The second pair starts with a minus.

So we take out −3, with the minus.

Both leave the same bracket, b + 4.

Careful!

If we take out 3, without the minus, we get −b − 4 in the bracket.

That does not match b + 4.

Take the minus out too.

Now both parts have b + 4 in them.

2 Same bracket out

b + 4 is in both parts, so we take it out once.

What is left, a − 3, goes in the other bracket.

So we get (b + 4)(a − 3).

3 Check

Let's check: we multiply it back out.

Each part of the first bracket times each part of the second.

We get ab + 4a − 3b − 12 again.

So the answer is right!

Let's look back.

First: group in pairs.

Then: same bracket out.

Last: check.