The expression given is:

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

Since both the numerator and denominator are squared terms, there isn't much simplification unless more details about \( x \) or \( y \) are provided. However, the expression is already in its simplest form unless you expand the squares.

### Expanded Form:
If we expand the squared terms, the numerator becomes:

\[
(2x - y)^2 = (2x)^2 - 2(2x)(y) + (y)^2 = 4x^2 - 4xy + y^2
\]

Similarly, the denominator becomes:

\[
(4 + 2x)^2 = (4)^2 + 2(4)(2x) + (2x)^2 = 16 + 16x + 4x^2
\]

Thus, the fully expanded form of the expression is:

\[
\frac{4x^2 - 4xy + y^2}{16 + 16x + 4x^2}
\]

If no further conditions are given, this is the expanded form of the original expression.

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Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How can this expression be used in a real-world application?
2. What happens to the expression if \( y = 2x \)?
3. Can this be factored back into its original form after expansion?
4. How do you calculate the derivative of this expression with respect to \( x \)?
5. What is the limit of the expression as \( x \to 0 \)?

**Tip:** Always double-check if an expression can be simplified before expanding, as some forms are more useful in their compact representation.

Learn how to simplify and expand the expression (2x - y)² ÷ (4 + 2x)². This detailed step-by-step solution breaks down the polynomial expansion process and examines how both numerator and denominator are expanded. Suitable for students in Grades 10-12.

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