Factorizing [tex]\( y^2 - xy + x - y \)[/tex]:
Step 1: Group the terms in pairs that have common factors.
[tex]\[ (y^2 - xy) + (x - y) \][/tex]
Step 2: Factor out the common factor from each pair.
[tex]\[ y(y - x) + 1(x - y) \][/tex]
Notice that [tex]\( (x - y) \)[/tex] can be seen as [tex]\(-(y - x)\)[/tex]:
[tex]\[ y(y - x) - 1(y - x) \][/tex]
Step 3: Factor out the common factor [tex]\( (y - x) \)[/tex]:
[tex]\[ (y - x)(y - 1) \][/tex]
Step 4: Simplify, keeping in mind that the negative sign distributes:
[tex]\[ - (x - y)(y - 1) \][/tex]
Therefore, the factorized form of the expression [tex]\( y^2 - xy + x - y \)[/tex] is:
[tex]\[ -(x - y)(y - 1) \][/tex]
