Factorize the following expression ab-a-b+1

Group 'em together

a b - a + 1 - b

a b - a = a (b - 1)

Notice that there will be a 1 as without it it'll simply be ab

1 - b = 1 (1 - b)

Notice that it doesn't match with the upper one ... so we'll change the signs

1 (1 - b) = - 1 (b - 1)

(try to multiply them now!

Jot them down in one expression

a (b - 1) - 1 (b - 1)

You get!

(a - 1) (b - 1)