To evaluate the expression [tex]\( t^2 + 8 r t + r^2 \)[/tex] when [tex]\( r = 3 \)[/tex] and [tex]\( t = 11 \)[/tex], follow these steps:
1. Substitute the values of [tex]\( r \)[/tex] and [tex]\( t \)[/tex] into the expression:
[tex]\[
(11)^2 + 8 \cdot (3) \cdot (11) + (3)^2
\][/tex]
2. Calculate [tex]\( t^2 \)[/tex]:
[tex]\[
11^2 = 121
\][/tex]
3. Calculate [tex]\( 8 r t \)[/tex]:
[tex]\[
8 \cdot 3 \cdot 11 = 8 \cdot 33 = 264
\][/tex]
4. Calculate [tex]\( r^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
5. Add all the results together:
[tex]\[
121 + 264 + 9
\][/tex]
6. Finally, sum these values:
[tex]\[
121 + 264 = 385
\][/tex]
[tex]\[
385 + 9 = 394
\][/tex]
Therefore, the value of the expression [tex]\( t^2 + 8 r t + r^2 \)[/tex] when [tex]\( r = 3 \)[/tex] and [tex]\( t = 11 \)[/tex] is [tex]\( \boxed{394} \)[/tex].
