Perform the operation(s) and simplify completely.

To simplify the expression \((-5x^2 + 7)(-5x^2 - 7) - 4(x^3 + 1)(2x + 3)\), we will perform step-by-step calculations.

Step 1: Expand \((-5x^2 + 7)(-5x^2 - 7)\)

Using the difference of squares: \[ (a+b)(a-b) = a^2 - b^2 \] Let \(a = -5x^2\) and \(b = 7\): \[ (-5x^2 + 7)(-5x^2 - 7) = (-5x^2)^2 - 7^2 = 25x^4 - 49. \]

Step 2: Expand \(4(x^3 + 1)(2x + 3)\)

First, expand \((x^3 + 1)(2x + 3)\) using the distributive property (FOIL method): \[ (x^3)(2x) + (x^3)(3) + (1)(2x) + (1)(3) = 2x^4 + 3x^3 + 2x + 3. \]

Next, multiply the entire expression by \(4\): \[ 4(2x^4 + 3x^3 + 2x + 3) = 8x^4 + 12x^3 + 8x + 12. \]

Step 3: Combine the two results

Now we combine both parts: \[ 25x^4 - 49 - (8x^4 + 12x^3 + 8x + 12). \]

Distributing the negative sign: \[ 25x^4 - 49 - 8x^4 - 12x^3 - 8x - 12 = (25x^4 - 8x^4) + (-12x^3) + (-8x) + (-49 - 12). \]

Step 4: Simplify the combined expression

Combine like terms: \[ (25x^4 - 8x^4) - 12x^3 - 8x - (49 + 12). \] \[ = 17x^4 - 12x^3 - 8x - 61. \]

Final Result

Thus, we have \[ 17x^4 - 12x^3 - 8x - 61. \]

The correct answer is: C. \(17x^4 - 12x^3 - 8x - 61\)