To multiply the complex numbers \((-10 + 5i)\) and \((-10 - 5i)\), we can use the formula for the product of two complex numbers, which is similar to multiplying binomials.
The expression can be multiplied as follows:
\[ (-10 + 5i)(-10 - 5i) = (-10)(-10) + (-10)(-5i) + (5i)(-10) + (5i)(-5i) \]
Now let's compute each term:
- \((-10)(-10) = 100\)
- \((-10)(-5i) = 50i\)
- \((5i)(-10) = -50i\)
- \((5i)(-5i) = -25i^2\)
Now, recall that \(i^2 = -1\). Therefore, we have:
\[ -25i^2 = -25(-1) = 25 \]
Putting it all together:
\[ 100 + 50i - 50i + 25 \]
The \(50i\) and \(-50i\) cancel each other out, so we are left with:
\[ 100 + 25 = 125 \]
Thus, the result of multiplying \((-10 + 5i)\) and \((-10 - 5i)\) is:
\[ \boxed{125} \]