(1)32x^3-2x =2x(16x^2-1)=2x(4x+1)(4x-1);(2)-14xy-x^2-49y^2 =-(x^2+14xy+49y^2)=-(x+7y)^2;(3)x^3-xy^2=x(x^2-y^2)=x(x+y)(x-y);(4)x^3-6x^2+9x=x(x^2-6x+9)=x(x-3)^2.