To simplify the expression 2sin(x)cos(x) - cos(x) - sin(x) + 1, we can use trigonometric identities to rewrite the terms in a more simplified form.

First, recall the double angle identity: sin(2x) = 2sin(x)cos(x). We can rewrite 2sin(x)cos(x) as sin(2x).

Now, the expression becomes sin(2x) - cos(x) - sin(x) + 1.

Next, we can use the trigonometric identity sin(2x) = 2sin(x)cos(x) to rewrite sin(2x) as 2sin(x)cos(x). The expression then becomes 2sin(x)cos(x) - cos(x) - sin(x) + 1.

And we can factor out a common factor of cos(x) from the first two terms: cos(x)(2sin(x) - 1) - sin(x) + 1.

Therefore, the simplified form of the expression 2sin(x)cos(x) - cos(x) - sin(x) + 1 is cos(x)(2sin(x) - 1) - sin(x) + 1.