To factor the expression [tex]\(xy - 4x + y - 4\)[/tex], follow these steps:
1. Group the terms: Start by grouping the terms to see common factors.
[tex]\[
xy - 4x + y - 4 = (xy - 4x) + (y - 4)
\][/tex]
2. Factor out the common factors from each group:
- From the first group [tex]\(xy - 4x\)[/tex], you can factor out [tex]\(x\)[/tex]:
[tex]\[
xy - 4x = x(y - 4)
\][/tex]
- From the second group [tex]\(y - 4\)[/tex], it’s already in its simplest form.
3. Combine the factored groups:
[tex]\[
xy - 4x + y - 4 = x(y - 4) + 1(y - 4)
\][/tex]
4. Factor out the common binomial factor: Notice that both terms have a common factor of [tex]\((y - 4)\)[/tex]:
[tex]\[
x(y - 4) + 1(y - 4) = (x + 1)(y - 4)
\][/tex]
Therefore, the factorized form of the expression [tex]\(xy - 4x + y - 4\)[/tex] is:
[tex]\[
(x + 1)(y - 4)
\][/tex]
