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