Factor 4xy + 8x + 12y + 24 Step by Step

Step by step

The question

Question: factor 4xy + 8x + 12y + 24.

There are four terms.

So we factor them in pairs.

This is called grouping.

4xy + 8x + 12y + 24

1 Take out the common factor

All four terms can be divided by 4.

So we take 4 out first, like in the common factor lesson.

4, 8, 12, 24: all in the 4 times table

So it is 4(xy + 2x + 3y + 6).

Now we group what is in the bracket.

= 4(xy + 2x + 3y + 6)

2 Group in pairs

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

= 4[(xy + 2x) + (3y + 6)]

From the first pair we take out x.

From the second pair we take out 3.

Both leave the same bracket, y + 2.

(xy + 2x) = x(y + 2)

(3y + 6) = 3(y + 2)

Now both parts have y + 2 in them.

= 4[x(y + 2) + 3(y + 2)]

Careful!

This is not the answer yet.

It is still two parts added.

Factored means one thing times another.

Careful: not done yet: still a + between two parts

3 Same bracket out

y + 2 is in both parts, so we take it out once.

What is left, x + 3, goes in the other bracket.

ab + cb = b(a + c)

So we get 4(y + 2)(x + 3).

= 4(y + 2)(x + 3)

4 Check

Let's check: we multiply it back out.

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

Then 4 times every term.

Check: 4(y + 2)(x + 3) = 4(xy + 3y + 2x + 6)

= 4(xy + 2x + 3y + 6) = 4xy + 8x + 12y + 24

We get 4xy + 8x + 12y + 24 again.

So the answer is right!

Let's look back.

First: take out the common factor.

Then: group in pairs.

Then: same bracket out.

Last: check.

Answer