Question

Express ax − a + x − 1 as a product of two binomials.

Answer 1

Ax - a + x - 1 = a(x - 1) + (x - 1) = (x - 1)(a + 1)
The answer is: (x - 1)(a + 1) 

Answer 2

In this case you can factorize the expresion using common factor twise as follows:

first factor $a$ in the two first terms and use the asociative law to associate the third and fourth terms:

$a(x-1) + (x-1)$

In the last expression, we have once again a common factor, namely $(x-1)$. So we factorize by common factor to obtain:

$(x-1)(a+1)$

and this complete the answer.