The problem is to simplify the expression $(x-3)^2 - (x+4)(x-4)$.

1. Problem Description

The problem is to simplify the expression $(x-3)^2 - (x+4)(x-4)$.

2. Solution Steps

First, we expand $(x-3)^2$ using the formula $(a-b)^2 = a^2 - 2ab + b^2$:

$(x-3)^2 = x^2 - 2(x)(3) + 3^2 = x^2 - 6x + 9$

Next, we expand $(x+4)(x-4)$ using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$:

$(x+4)(x-4) = x^2 - 4^2 = x^2 - 16$

Now, substitute these expressions back into the original expression:

$(x-3)^2 - (x+4)(x-4) = (x^2 - 6x + 9) - (x^2 - 16)$

Distribute the negative sign:

$x^2 - 6x + 9 - x^2 + 16$

Combine like terms:

$(x^2 - x^2) - 6x + (9 + 16) = 0x^2 - 6x + 25 = -6x + 25$

3. Final Answer

$-6x + 25$