The expression given is:

\[ 8 - y^2 \]

This expression is a difference of squares and can be factored. Here's the detailed process:

1. **Identify the Difference of Squares**: The expression \( 8 - y^2 \) is in the form of \( a^2 - b^2 \), where \( a^2 = 8 \) and \( b^2 = y^2 \).

2. **Rewrite as a Difference of Squares**: However, to factor it directly, \( 8 \) is not a perfect square. So, let's leave it as is or you could approximate or solve as needed for specific cases.

   The expression can be factored as:
   
   \[
   8 - y^2 = (\sqrt{8} - y)(\sqrt{8} + y)
   \]

   If you simplify further:
   
   \[
   = (2\sqrt{2} - y)(2\sqrt{2} + y)
   \]

3. **Multiplication by 2**: If the expression needs to be multiplied by 2, as indicated by the "×2" at the beginning:

   \[
   2 \times (8 - y^2) = 16 - 2y^2
   \]

This is the fully simplified expression after applying the multiplication.

Would you like to dive into any more details or have questions on this? Here are some related questions you might find interesting:

1. How do you handle differences of squares when one term isn't a perfect square?
2. What are the methods to approximate square roots in algebraic expressions?
3. How does multiplying a quadratic expression by a constant affect its graph?
4. What are the rules for factoring quadratic expressions with coefficients?
5. How does completing the square work for non-perfect squares?

**Tip:** When dealing with quadratic expressions that involve square roots, consider whether exact or approximate solutions are needed based on the context of the problem.

Explore how to factor the expression 8 - y^2 using the difference of squares method. This problem involves algebraic manipulation and understanding of square roots. Suitable for high school students studying algebra and quadratic equations.

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