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

Let's dive right into factoring! For the first expression, \(3a^{2} - 6a^{2}b\), factor out the common term \(3a^{2}\): \(3a^{2}(1 - 2b)\). In the second expression, \(2x^{3} + 4x^{2} + 6x\), you can factor out \(2x\): \(2x(x^{2} + 2x + 3)\). Moving on to \(4x - 4\), it can simply be written as: \(4(x - 1)\). Next up, for \(y^{2} - y^{2} - y\), notice that \(y^{2} - y^{2} = 0\), leaving you with: \(-y\). For \(10x - 5y + 35\), factor out the number 5: \(5(2x - y + 7)\). Finally, in the expression \(3x^{2}y - 5xy^{2}\), you can factor out \(xy\): \(xy(3x - 5y)\). And voila! You’ve got all the factored forms!