The trinomial you're dealing with is:

\[
B^2 + 16B + 64
\]

To factor this trinomial, follow these steps:

1. Identify the structure of the trinomial: \( B^2 + 16B + 64 \). Notice that this is in the form of \( x^2 + 2ab + b^2 \).
   
2. Recognize the perfect square pattern: The first term \( B^2 \) is a square, and the third term \( 64 \) is also a square because \( 64 = 8^2 \).

3. Rewrite the middle term: The middle term \( 16B \) is twice the product of \( B \) and \( 8 \), since \( 2 \times B \times 8 = 16B \).

Thus, we can factor the trinomial as:

\[
(B + 8)^2
\]

So, \( B^2 + 16B + 64 \) factors into \( (B + 8)(B + 8) \), or more simply:

\[
(B + 8)^2
\]

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. How do you factor trinomials when they aren't perfect squares?
2. What is the difference between factoring perfect square trinomials and other types of trinomials?
3. Can trinomials have more than one valid factorization?
4. How do you solve equations using factored trinomials?
5. What happens when a trinomial cannot be factored over the integers?

**Tip:** When factoring trinomials, always check for perfect square patterns as it simplifies the process significantly.

Learn how to factor the trinomial B^2 + 16B + 64 using the perfect square trinomial method. This step-by-step guide walks through recognizing the structure, identifying squares, and rewriting the expression as (B + 8)^2. Ideal for students in Grades 8-10.

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