$\begin{array}{l}a)\,\,3x^2y - 6xy^2\\ = 3xy.x - 3xy.2y\\ = 3xy(x - 2y)\\ b)\,\,3x - 3y + x^2 - y^2\\ = (3x - 3y) + (x^2 -y^2)\\ = 3(x-y) + (x-y)(x+y)\\ = (x-y)(3 + x + y)\\ c)\,\,x^2 + 3x + 2\\ = x^2 + x + 2x + 2\\ = (x^2 + x) + (2x + 2)\\ = x(x+1) + 2(x+1)\\ = (x+1)(x+2)\end{array}$