Simplify the expression $(x-5)^2 - (x+2)(x-2)$.

1. Problem Description

Simplify the expression $(x-5)^2 - (x+2)(x-2)$.

2. Solution Steps

First, expand $(x-5)^2$:

$(x-5)^2 = (x-5)(x-5) = x^2 - 5x - 5x + 25 = x^2 - 10x + 25$

Next, expand $(x+2)(x-2)$. This is a difference of squares:

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

Now, subtract the second expression from the first:

$(x-5)^2 - (x+2)(x-2) = (x^2 - 10x + 25) - (x^2 - 4)$

$= x^2 - 10x + 25 - x^2 + 4$

$= (x^2 - x^2) - 10x + (25 + 4)$

$= 0 - 10x + 29$

$= -10x + 29$

3. Final Answer

The simplified expression is $-10x + 29$.

So, the answer is c) $-10x+29$.