The given expression to factor is:

$x^2 + 16x + 64$

This is a quadratic expression, and we can try factoring it as a perfect square trinomial. Notice that:

$64 = 8^2 \quad \text{and} \quad 16x = 2 \times 8 \times x$

This matches the form of $(x + a)^2 = x^2 + 2ax + a^2$, where $a = 8$.

Thus, the factored form is:

$(x + 8)^2$

So, the factored expression is:

$(x + 8)(x + 8) \quad \text{or simply} \quad (x + 8)^2$

Would you like further details or clarification on the steps?

Here are five related questions:

1. How do you identify perfect square trinomials?
2. Can all quadratic expressions be factored as perfect squares?
3. What if the middle term was negative, how would the factoring change?
4. How can you check if your factored expression is correct?
5. What other factoring techniques could be applied if the trinomial was not a perfect square?

Tip: Always check if a quadratic expression fits the form $(x + a)^2$ or $(x - a)^2$ when factoring!