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The expression provided is \( x^2 + 16x + 64 \).

To factor it completely, we need to find two numbers that multiply to 64 and add to 16.

The numbers 8 and 8 satisfy these conditions because:
- \( 8 \times 8 = 64 \)
- \( 8 + 8 = 16 \)

Thus, the expression can be factored as:
\[
x^2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)^2
\]

So, the complete factorization of \( x^2 + 16x + 64 \) is \( (x + 8)^2 \).

Would you like any more details or have any questions? Here are some related questions to consider:

1. How can you verify the factorization of a quadratic expression?
2. What are the steps to factor a quadratic trinomial in general?
3. What is the significance of a perfect square trinomial?
4. How does factoring relate to solving quadratic equations?
5. How would the factorization change if the middle term were negative?

**Tip:** Always check if a quadratic trinomial can be factored as a perfect square by comparing the middle term to twice the square root of the constant term.

Learn how to factor the quadratic expression x^2 + 16x + 64 completely using the perfect square trinomial method. This guide provides a step-by-step solution suitable for students in Grades 8-10.

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