To determine the value of [tex]\((7m - 5n)^3 - (7m + 5n)^3\)[/tex], let's break it down step by step.
We start with the expressions:
- [tex]\((7m - 5n)^3\)[/tex]
- [tex]\((7m + 5n)^3\)[/tex]
Next, remember that we aim to find the result of their difference:
[tex]\[ (7m - 5n)^3 - (7m + 5n)^3 \][/tex]
Given the final result, we have:
[tex]\[ (7m - 5n)^3 - (7m + 5n)^3 = -1470m^2 n - 250n^3 \][/tex]
Now, comparing this result with the given multiple choices:
A) [tex]\( 1470 m^2 n - 250 n^3 \)[/tex]
B) [tex]\( 1470 m^2 n + 250 n^3 \)[/tex]
C) [tex]\( -1470 m^2 n - 250 n^3 \)[/tex]
D) [tex]\( -1470 m^2 n + 250 n^3 \)[/tex]
The correct choice corresponding to [tex]\(-1470m^2 n - 250n^3\)[/tex] is:
C) [tex]\(-1470 m^2 n - 250 n^3\)[/tex]
Thus, the correct answer is:
C) [tex]\( -1470 m^2 n - 250 n^3 \)[/tex]
