How can I determine the factorization of an algebraic expression that contains parentheses?

Question

I am trying to complete a exercise, but I can not figure out what the required steps are to determine the factorization of the following expressions:

$$(a+1)b-3(a+1)$$ $$a(b-1)-2(b-1)$$ $$2a(b+4)+7(b+4)$$ $\phantom{asd}$

Answer 1

It is very simple:

Put $x=a+1;y=b-1;z=b+4$

Then we have

$(a+1)b-3(a+1)=xb-3b=x(b-3)=(a+1)(b-3)$

$a(b-1)-2(b-1)=ay-2y=y(a-2)=(b-1)(a-2)$

...

Of course, you won't even need to put extra variables at all if you can notice that there is a common expression between all the terms.

Answer 2

Since $(a+1)$ is common to both terms in the first expression, we can factor it out to get: $$(a+1)(b-3)$$ Can you do the same for the other two?