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We are given the following expression:

\[
\frac{y^2 - 16}{y^2 + 8y + 16} \times \frac{y + 4}{y^2 - 8y + 16}
\]

### Step 1: Factor each term

1. **First numerator**: \( y^2 - 16 \) is a difference of squares, so:
   \[
   y^2 - 16 = (y - 4)(y + 4)
   \]

2. **First denominator**: \( y^2 + 8y + 16 \) is a perfect square trinomial, so:
   \[
   y^2 + 8y + 16 = (y + 4)^2
   \]

3. **Second denominator**: \( y^2 - 8y + 16 \) is also a perfect square trinomial, so:
   \[
   y^2 - 8y + 16 = (y - 4)^2
   \]

### Step 2: Rewrite the expression with factored terms

\[
\frac{(y - 4)(y + 4)}{(y + 4)^2} \times \frac{y + 4}{(y - 4)^2}
\]

### Step 3: Simplify by canceling common factors

- The factor \( (y + 4) \) appears once in the numerator and once in the denominator, so cancel one \( (y + 4) \).
- Similarly, the factor \( (y - 4) \) appears in both, so cancel one \( (y - 4) \).

After canceling, we are left with:

\[
\frac{1}{(y + 4)(y - 4)} = \frac{1}{y^2 - 16}
\]

### Final Answer:

The simplified expression is:

\[
\frac{1}{y^2 - 16}
\]

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Would you like more details on any of these steps? 

Here are 5 related questions:
1. How do you factor a difference of squares?
2. What are perfect square trinomials, and how do you factor them?
3. Can you always simplify complex rational expressions by canceling factors?
4. What happens if a variable in the denominator equals zero?
5. How do you multiply two rational expressions?

**Tip:** Always check for common factors before multiplying rational expressions, as canceling early can save time.

Simplify the expression: (y^2 - 16) / (y^2 + 8y + 16) × (y + 4) / (y^2 - 8y + 16)

Learn how to simplify a rational expression by factoring a difference of squares and perfect square trinomials. This algebraic problem covers key concepts of factoring and rational expression simplification, suitable for students in Grades 9-11.

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