To find the difference of the given expressions [tex]\( (3 - 13x - 7x^2) - (5x^2 + 12x - 10) \)[/tex], follow these steps:
1. Distribute the negative sign to the terms in the second expression:
[tex]\[
(3 - 13x - 7x^2) - 5x^2 - 12x + 10
\][/tex]
This transforms our expression into:
[tex]\[
3 - 13x - 7x^2 - 5x^2 - 12x + 10
\][/tex]
2. Combine like terms:
- Combine the [tex]\( x^2 \)[/tex] terms:
[tex]\[
-7x^2 - 5x^2 = -12x^2
\][/tex]
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[
-13x - 12x = -25x
\][/tex]
- Combine the constant terms:
[tex]\[
3 + 10 = 13
\][/tex]
3. Write down the simplified expression:
[tex]\[
-12x^2 - 25x + 13
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{-12x^2 - 25x + 13}
\][/tex]
So, the correct option is D.
