Factor by grouping: 5a^2 -5bc-5ab+5ac?

Question

Factor by grouping: 5a^2 -5bc-5ab+5ac

Answer 1

Start by factoring out a 5 to get
5(a^2-bc-ab+ac)
Rearrange the terms inside the parentheses like this:
5(a^2-ab-bc +ac)
In essence, what you are trying to do is see if you can get the terms that have like variables together and then factor.
from here
5 a(a-b) - c(a+b)
we can simply change the sign from a - to a + and reverse all the signs inside the second term:
5a(a-b)+c(a-b)
Now, we can treat the (a-b) as if it were just one term and we end up with:
(5a+c)(a-b)

If you want to double check your work, you can always FOIL and see if you come out with the original result

Answer 2

5a^2 - 5ab + 5ac - 5bc
5a(a-b) + 5c(a-b)
5(a+c)(a-b)