The expression \( a^2 + 8a + 16 \) is a quadratic expression. To simplify or factor it, you can look for two numbers that multiply to the constant term \( 16 \) and add to the coefficient of the linear term \( 8 \).

Here’s how you can factor it:

1. **Identify the factors:** 
   - The constant term is \( 16 \).
   - The middle term’s coefficient is \( 8 \).

   The numbers that multiply to \( 16 \) and add to \( 8 \) are \( 4 \) and \( 4 \).

2. **Factor the expression:**
   \[
   a^2 + 8a + 16 = (a + 4)(a + 4) = (a + 4)^2
   \]

So, the expression \( a^2 + 8a + 16 \) can be factored as \( (a + 4)^2 \).

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

1. How do you factor quadratic expressions in general?
2. What are the properties of perfect square trinomials?
3. How can you expand \( (a + b)^2 \) to verify the factorization?
4. What if the quadratic expression cannot be factored easily? What methods can be used?
5. How does completing the square work, and when is it useful?

**Tip:** When factoring quadratics, always check if the middle term can be split into two terms that add up to it and multiply to the constant term—this can indicate a perfect square trinomial.

Learn how to factor the quadratic expression a^2 + 8a + 16 using the method of identifying factors and factoring perfect square trinomials. This problem covers key algebraic concepts, including the quadratic formula and factorization theorems. Suitable for students in Grades 7-9.

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