First, you rearrange the terms so that ones with a common factor are together.

= A(b+1) + 4(1+b) (we have factored the first 2 terms, and the last 2 terms. We recognize that 1+b = b+1, so we can factor once more.)

**Ab + 4 + A + 4b**= Ab + A + 4 + 4b (we have swapped the order of the middle two terms to get the order we want)= A(b+1) + 4(1+b) (we have factored the first 2 terms, and the last 2 terms. We recognize that 1+b = b+1, so we can factor once more.)

**= (A+4)(b+1)**