(x-1)(y%2B1)-xy-factor.jpeg "(xy-1)(x-1)(y+1)-xy Factor")
Factoring (xy-1)(x-1)(y+1)-xy
This expression can be factored to reveal a simpler form. Let's break down the steps:
Step 1: Expand the expression
Begin by expanding the first three terms of the expression:
(xy-1)(x-1)(y+1)-xy = (xy-1)(x(y+1)-(y+1))-xy
Further simplification:
(xy-1)(xy+x-y-1)-xy = x^2y^2 + x^2y - xy^2 - xy - xy - x + y + 1 - xy
Step 2: Combine like terms
Now combine all the similar terms:
x^2y^2 + x^2y - xy^2 - 3xy - x + y + 1
Step 3: Factor by grouping
Group the terms to facilitate factoring:
(x^2y^2 - xy^2) + (x^2y - 3xy) + (-x + y + 1)
Factor out common terms from each group:
xy^2(x-1) + xy(x-3) + (-x + y + 1)
Step 4: Recognize a common factor
Notice that the last three terms are the negative of the first three terms. We can rewrite them by factoring out a -1:
xy^2(x-1) + xy(x-3) - (x - y - 1)
Now we have a common factor of (x-1) in the first two terms and a common factor of -(x-1) in the last term:
(x-1)(xy^2 + xy -1)
Final Factored Form
Therefore, the factored form of the expression is:
(x-1)(xy^2 + xy -1)