Step by step
The question
Question: factor ab + 5a + 2b + 10.
There are four terms.
So we factor them in pairs.
This is called grouping.
ab + 5a + 2b + 10
1 Group in pairs
We put the first two together, and the last two together.
= (ab + 5a) + (2b + 10)
From the first pair we take out a.
From the second pair we take out 2.
Both leave the same bracket, b + 5.
(ab + 5a) = a(b + 5)
(2b + 10) = 2(b + 5)
Now both parts have b + 5 in them.
= a(b + 5) + 2(b + 5)
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
b + 5 is in both parts, so we take it out once.
What is left, a + 2, goes in the other bracket.
ab + cb = b(a + c)
So we get (b + 5)(a + 2).
= (b + 5)(a + 2)
3 Check
Let's check: we multiply it back out.
Each part of the first bracket times each part of the second.
Check: (b + 5)(a + 2) = ab + 2b + 5a + 10
= ab + 5a + 2b + 10
We get ab + 5a + 2b + 10 again.
So the answer is right!
Let's look back.
First: group in pairs.
Then: same bracket out.
Last: check.
Answer
= (b + 5)(a + 2)