Factor. $$ \begin{array}{ll}3 a^{2}-6 a^{2} b= & 2 x^{3}+4 x^{2}+6 x= \ 4 x-4= & y^{2}-y^{2}-y= \ 10 x-5 y+35= & 3 x^{2} y-5 x y^{2}=\end{array} $$

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Sure, let's factor each of the given expressions step by step.

1. **$$ 3a^{2} - 6a^{2}b $$**

- **Factor out the greatest common factor (GCF):**
     $$
     3a^{2}(1 - 2b)
     $$
   
2. **$$ 2x^{3} + 4x^{2} + 6x $$**

- **Factor out the GCF:**
     $$
     2x(x^{2} + 2x + 3)
     $$
   - **Note:** The quadratic $$ x^{2} + 2x + 3 $$ does not factor further over the real numbers.

3. **$$ 4x - 4 $$**

- **Factor out the GCF:**
     $$
     4(x - 1)
     $$
   
4. **$$ y^{2} - y^{2} - y $$**

- **Simplify the expression first:**
     $$
     y^{2} - y^{2} - y = -y
     $$
   - **So, it's already factored as:**
     $$
     -y
     $$
   
5. **$$ 10x - 5y + 35 $$**

- **Factor out the GCF (which is 5):**
     $$
     5(2x - y + 7)
     $$
   
6. **$$ 3x^{2}y - 5xy^{2} $$**

- **Factor out the GCF (which is $$ xy $$):**
     $$
     xy(3x - 5y)
     $$

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**Summary of Factored Forms:**

1. $$ 3a^{2} - 6a^{2}b = 3a^{2}(1 - 2b) $$

2. $$ 2x^{3} + 4x^{2} + 6x = 2x(x^{2} + 2x + 3) $$

3. $$ 4x - 4 = 4(x - 1) $$

4. $$ y^{2} - y^{2} - y = -y $$

5. $$ 10x - 5y + 35 = 5(2x - y + 7) $$

6. $$ 3x^{2}y - 5xy^{2} = xy(3x - 5y) $$
Here are the factored forms of the given expressions: 1. $$ 3a^{2} - 6a^{2}b = 3a^{2}(1 - 2b) $$ 2. $$ 2x^{3} + 4x^{2} + 6x = 2x(x^{2} + 2x + 3) $$ 3. $$ 4x - 4 = 4(x - 1) $$ 4. $$ y^{2} - y^{2} - y = -y $$ 5. $$ 10x - 5y + 35 = 5(2x - y + 7) $$ 6. $$ 3x^{2}y - 5xy^{2} = xy(3x - 5y) $$

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