### Instruction: Evaluate $(2 + 1)(2^2 + 1^2)(2^4 + 1^4)$.### Response: This looks like a product of three factors, each of which has the form $2^k + 1^k$ for some power of $k$.
I wonder if there is a pattern or a shortcut to simplify these factors.
I notice that the first factor, $2 + 1$, is just $3$.
The second factor, $2^2 + 1^2$, is $4 + 1$, which is $5$.
The third factor, $2^4 + 1^4$, is $16 + 1$, which is $17$.
So the product is $3 \times 5 \times 17$.
I could multiply these numbers in any order, but I think it might be easier to start with $3 \times 5$, which is $15$.
Then I can multiply $15 \times 17$.
To do this, I can use the distributive property and write $15 \times 17 = (10 + 5) \times 17 = 10 \times 17 + 5 \times 17$.
I know that $10 \times 17 = 170$ and $5 \times 17 = 85$.
So $15 \times 17 = 170 + 85 = 255$.
Therefore, the final answer is $255$.