Step by step
The question
Question: factor xy + 2x + 4y + 8.
There are four terms.
So we factor them in pairs.
This is called grouping.
xy + 2x + 4y + 8
1 Group in pairs
We put the first two together, and the last two together.
= (xy + 2x) + (4y + 8)
From the first pair we take out x.
From the second pair we take out 4.
Both leave the same bracket, y + 2.
(xy + 2x) = x(y + 2)
(4y + 8) = 4(y + 2)
Now both parts have y + 2 in them.
= x(y + 2) + 4(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
2 Same bracket out
y + 2 is in both parts, so we take it out once.
What is left, x + 4, goes in the other bracket.
ab + cb = b(a + c)
So we get (y + 2)(x + 4).
= (y + 2)(x + 4)
3 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
Check: (y + 2)(x + 4) = xy + 4y + 2x + 8
= xy + 2x + 4y + 8
We get xy + 2x + 4y + 8 again.
So the answer is right!
Let's look back.
First: group in pairs.
Then: same bracket out.
Last: check.
Answer
= (y + 2)(x + 4)