To find the value of the expression [tex]\(-3|15-s|+2s^3\)[/tex] when [tex]\(s = -3\)[/tex], follow these steps:
1. Substitute [tex]\( s = -3 \)[/tex] into the expression.
So, the expression becomes:
[tex]\[
-3|15-(-3)| + 2(-3)^3
\][/tex]
2. Simplify the absolute value term [tex]\( |15 - (-3)| \)[/tex]:
[tex]\[
|15 - (-3)| = |15 + 3| = |18| = 18
\][/tex]
3. Substitute the value of the absolute value term back into the expression:
[tex]\[
-3 \cdot 18 + 2(-3)^3
\][/tex]
4. Calculate [tex]\(-3 \cdot 18\)[/tex]:
[tex]\[
-3 \cdot 18 = -54
\][/tex]
5. Compute the value of [tex]\(2(-3)^3\)[/tex]:
[tex]\[
(-3)^3 = -27 \quad \text{and} \quad 2 \cdot (-27) = -54
\][/tex]
6. Combine the results from the previous steps:
[tex]\[
-54 + (-54) = -108
\][/tex]
Therefore, the value of the expression [tex]\(-3|15-s|+2s^3\)[/tex] when [tex]\(s = -3\)[/tex] is [tex]\(\boxed{-108}\)[/tex].
