\(1,xy^3-x^3y=xy\left(y^2-x^2\right)=xy\left(y-x\right)\left(y+x\right)\\ 2,15xy+20x^2-30x=5x\left(3y+4x-6\right)\\ 3,6x-3xy=3x\left(2-y\right)\\ 4,x^3+2x^2+x=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\\ 4x^3-12x^2+9x=x\left(4x^2-12x+9\right)=x\left(2x-3\right)^2\\ 6,2x^2y+4xy^2-10x^3y^2=2xy\left(x+2y-5x^2y\right)\\ 7,x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
\(8,x^2\left(x-2y\right)+3x\left(x-2y\right)=\left(x^2+3x\right)\left(x-2y\right)=x\left(x+3\right)\left(x-2y\right)\\ 9,\left(5x+2\right)\left(x-3\right)-x\left(x-3\right)=\left(x-3\right)\left(5x+2-x\right)=\left(x-3\right)\left(4x+2\right)=2\left(x-3\right)\left(2x+1\right)\\ 10,\left(5x-3\right)\left(x+2\right)-2x\left(x+2\right)=\left(x+2\right)\left(5x-3-2x\right)=\left(x+2\right)\left(3x-3\right)=3\left(x+2\right)\left(x-1\right)\\ 11,x\left(x-1\right)-y\left(1-x\right)=x\left(x-1\right)+y\left(x-1\right)=\left(x-1\right)\left(x+y\right)\)
