Step by step
The question
Question: factor xy + 3x + 2y + 6.
There are four terms.
So we factor them in pairs.
This is called grouping.
xy + 3x + 2y + 6
1 Group in pairs
We put the first two together, and the last two together.
= (xy + 3x) + (2y + 6)
From the first pair we take out x.
From the second pair we take out 2.
Both leave the same bracket, y + 3.
(xy + 3x) = x(y + 3)
(2y + 6) = 2(y + 3)
Now both parts have y + 3 in them.
= x(y + 3) + 2(y + 3)
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 + 3 is in both parts, so we take it out once.
What is left, x + 2, goes in the other bracket.
ab + cb = b(a + c)
So we get (y + 3)(x + 2).
= (y + 3)(x + 2)
3 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
Check: (y + 3)(x + 2) = xy + 2y + 3x + 6
= xy + 3x + 2y + 6
We get xy + 3x + 2y + 6 again.
So the answer is right!
Let's look back.
First: group in pairs.
Then: same bracket out.
Last: check.
Answer
= (y + 3)(x + 2)