To evaluate the expression \( -16tu + 14u \) for \( t = -16 \) and \( u = -2 \), we first substitute the values of \( t \) and \( u \) into the expression.
- Substitute \( t = -16 \) and \( u = -2 \):
\[ -16(-16)(-2) + 14(-2) \]
- Calculate \( tu \):
\[ tu = -16 \cdot -2 = 32 \]
- Now substitute \( tu \) back into the expression:
\[ -16 \cdot 32 + 14(-2) \]
- Calculate \( -16 \cdot 32 \):
\[ -16 \cdot 32 = -512 \]
- Calculate \( 14(-2) \):
\[ 14 \cdot -2 = -28 \]
- Substitute these results back into the expression:
\[ -512 - 28 \]
- Combine the terms:
\[ -512 - 28 = -540 \]
Thus, the simplified answer is:
\[ \boxed{-540} \]