Use the Distributive Property to factor out the greatest common factor for the expression $$ 100 x+ $$ $$ 200 y $$. $$ 50(2 x+4 y) $$ $$ 10(10 x+20 y) $$ $$ 100(x+2 y) $$ $$ 100(10 x+20 y) $$

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To factor out the greatest common factor (GCF) from the expression $$ 100x + 200y $$, we will follow these steps:

1. **Identify the GCF**: 
   - The coefficients of the terms are 100 and 200. The GCF of 100 and 200 is 100.
   - The variables involved are $$ x $$ and $$ y $$, which do not have a common factor.

2. **Factor out the GCF**:
   - We can express the original expression as:
   $$
   100x + 200y = 100(x + 2y)
   $$

Now, let's compare this with the provided options:

1. $$ 50(2x + 4y) $$
2. $$ 10(10x + 20y) $$
3. $$ 100(x + 2y) $$
4. $$ 100(10x + 20y) $$

The correct factored form of $$ 100x + 200y $$ is:

$$
100(x + 2y)
$$

Thus, the answer is:

**$$ 100(x + 2y) $$**.
$$ 100(x + 2y) $$

Use the Distributive Property to factor out the greatest common factor for the expression \( 100 x+ \) \( 200 y \). \( 50(2 x+4 y) \) \( 10(10 x+20 y) \) \( 100(x+2 y) \) \( 100(10 x+20 y) \)

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