Factorization "$(a -1)(b -1)$"

Question

I need to factorize $ab -a -b +1$. I know that the answer is $(a -1)(b -1)$ can anyone give me some tips on how to do it?

Answer 1

$ab-a-b+1=a(b-1)-(b-1)=a(b-1)-1(b-1)=(a-1)(b-1)$

Answer 2

You can apply the distributive law twice: \begin{align*} ab - a - b +1 = a(b-1) - (b-1) = (a-1)(b-1) \end{align*}