Factoring and Simplifying the Expression (xy1)(x1)(y+1)xy
This article explores the process of factoring and simplifying the given expression: (xy1)(x1)(y+1)xy.
Expanding the Expression
We can begin by expanding the expression using the distributive property:

Expand (xy1)(x1): (xy1)(x1) = xy(x1)  1(x1) = x²y  xy  x + 1

Multiply the expanded result by (y+1): (x²y  xy  x + 1)(y+1) = x²y(y+1)  xy(y+1)  x(y+1) + 1(y+1) = x²y² + x²y  xy²  xy  xy  x + y + 1

Combine like terms and subtract xy: x²y² + x²y  xy²  xy  xy  x + y + 1  xy = x²y² + x²y  xy²  3xy  x + y + 1
Factoring the Expression
While the expression can be simplified to the form above, it's not fully factored. Let's attempt to factor it further:

Look for common factors: The expression doesn't have any common factors that can be factored out.

Try grouping terms: We can try grouping terms to see if we can factor by grouping. However, this method doesn't lead to a straightforward factorization.

Consider the original form: The original form of the expression (xy1)(x1)(y+1)xy might be the most simplified and factored form.
Conclusion
The expression (xy1)(x1)(y+1)xy can be expanded and simplified to x²y² + x²y  xy²  3xy  x + y + 1. However, it doesn't seem to have a simpler factored form that can be easily obtained through standard factorization techniques. The original form of the expression might be considered the most concise and factored representation.