a) To simplify the expression x^2 - y^2 - 2x - 2y, we can factor the expression by grouping:

x^2 - y^2 - 2x - 2y
= (x^2 - 2x) - (y^2 + 2y)
= x(x - 2) - y(y + 2)
= x(x - 2) - y(-1)(y + 2)
= x(x - 2) + y(y + 2)

So the simplified expression is x(x - 2) + y(y + 2).

b) To simplify the expression x^2 - 9 - x^2(x^2 - 9), we can first distribute the -1 to the terms inside the parentheses:

x^2 - 9 - x^2(x^2 - 9)
= x^2 - 9 - x^2 * x^2 + x^2 * 9
= x^2 - 9 - x^4 + 9x^2

Next, we can combine like terms:

= (x^2 + 9x^2) - x^4 - 9
= 10x^2 - x^4 - 9

So the simplified expression is 10x^2 - x^4 - 9.