The expression given is $x^2 + 16x + 64$. To factor this, we need to look for two numbers that multiply to give 64 and add to give 16.

Step-by-step factoring:

1. Notice that $x^2 + 16x + 64$ is a perfect square trinomial.
2. The square root of 64 is 8, and 16 is twice 8.
3. This suggests that the expression can be factored as: $(x + 8)^2$

So, the factored form of $x^2 + 16x + 64$ is: $(x + 8)(x + 8) \quad \text{or} \quad (x + 8)^2$

Would you like more details on this process or any clarifications?

Here are 5 related questions you could explore:

1. How do you recognize a perfect square trinomial?
2. What is the process to factor quadratic expressions that are not perfect squares?
3. How does completing the square work for quadratic equations?
4. Can you use the quadratic formula to factor expressions like this?
5. How do you check if a factoring solution is correct?

Tip: When factoring quadratic trinomials, always check for perfect square trinomials first, as they simplify the process significantly.