Let's solve the given mathematical expression step-by-step:
The expression we need to evaluate is:
[tex]\[ s \cdot p \cdot q \cdot r \cdot (p+q) \cdot (q+r) \cdot (r+p) \div 104 \][/tex]
Given the values:
[tex]\[ s = 2 \][/tex]
[tex]\[ p = 1 \][/tex]
[tex]\[ q = 1 \][/tex]
[tex]\[ r = 1 \][/tex]
1. Evaluate individual components:
- First, we need to calculate [tex]\( p \cdot q \cdot r \)[/tex]:
[tex]\[
p \cdot q \cdot r = 1 \cdot 1 \cdot 1 = 1
\][/tex]
- Next, we calculate [tex]\( (p+q) \)[/tex]:
[tex]\[
p + q = 1 + 1 = 2
\][/tex]
- Then, [tex]\( (q+r) \)[/tex]:
[tex]\[
q + r = 1 + 1 = 2
\][/tex]
- Finally, [tex]\( (r+p) \)[/tex]:
[tex]\[
r + p = 1 + 1 = 2
\][/tex]
2. Multiply these results together:
- Combine the above results:
[tex]\[
p \cdot q \cdot r \cdot (p+q) \cdot (q+r) \cdot (r+p) = 1 \cdot 2 \cdot 2 \cdot 2 = 8
\][/tex]
3. Multiply by [tex]\( s \)[/tex]:
- Now include the value of [tex]\( s \)[/tex]:
[tex]\[
s \cdot (p \cdot q \cdot r \cdot (p+q) \cdot (q+r) \cdot (r+p)) = 2 \cdot 8 = 16
\][/tex]
4. Divide by 104:
- Finally, we divide the result by 104:
[tex]\[
\frac{16}{104} = 0.15384615384615385
\][/tex]
So, the detailed calculation leads us to the result:
[tex]\[ \operatorname{Result} = 0.15384615384615385 \][/tex]
and the polynomial part evaluated is:
[tex]\[ \text{Polynomial Value} = 8 \][/tex]
