## Factoring the Expression (xy+1)(x+1)(y+1)+xy

The expression (xy+1)(x+1)(y+1)+xy can be factored into a simpler form. Here's how to do it:

**Expand the expression:**

- Start by expanding the first part of the expression: (xy+1)(x+1)(y+1) = (x^2y + xy + x + 1)(y+1)
- Then, multiply the result by (y+1): x^2y^2 + x^2y + xy^2 + xy + xy + x + y + 1.
- Now we have the complete expanded expression: x^2y^2 + x^2y + xy^2 + 2xy + x + y + 1 + xy.

**Rearrange the terms:**

- Group the terms that have common factors: (x^2y^2 + xy^2) + (x^2y + 2xy + x) + (y + 1).

**Factor out common factors:**

- From the first group, factor out xy^2: xy^2(x+1).
- From the second group, factor out x: x(xy + 2y + 1).
- The third group remains as it is: (y+1).

**Combine the factored terms:**

- The expression now looks like this: xy^2(x+1) + x(xy + 2y + 1) + (y+1).
- Notice that the term (x+1) appears in the first term and the term (y+1) appears in the third term.

**Factor by grouping:**

- Group the first and third terms: [xy^2(x+1) + (y+1)] + x(xy + 2y + 1)
- Factor out (x+1) from the first group and x from the second group: (x+1)(xy^2+1) + x(xy+2y+1)

**Final factorization:**

- We can see that (xy+1) is a common factor in both terms.
- Factor out (xy+1):
**(xy+1)(x+1+x(y+1))**

Therefore, the factored form of the expression (xy+1)(x+1)(y+1)+xy is **(xy+1)(x+1+x(y+1))**.