1,\(x^3-4x^2+4x=x\left(x^2-4x+4\right)=x\left(x^2-2.x.2+2^2\right)=x\left(x-2\right)^2\)
2,\(x^3-6x^2+9x=x\left(x^2-6x+9\right)=x\left(x^2-2.x.3+3^2\right)=x\left(x-3\right)^2\)
3,\(x^2-8x-9=x^2+x-9x-9=x\left(x+1\right)-9\cdot\left(x+1\right)=\left(x-9\right).\left(x+1\right)\)4,
\(x^2-4xy+3y^2=x^2-xy-3xy+3y^2=x\left(x-y\right)-3y\left(x-y\right)=\left(x-y\right).\left(x-3y\right)\)5, \(2x^2+3xy-5y^2=2x^2-2xy+5xy-5y^2=2x\left(x-y\right)+5y\left(x-y\right)=\left(x-y\right).\left(2x+5y\right)\)6,\(\left(x+y\right)^3-x^3-y^3=x^3+3x^2y+3xy^2+y^3-x^3-y^3=3xy\left(x+y\right)\)
7,\(x^3-y^3+2x^2-2y^2=\left(x-y\right)\left(x^2+y^2+xy\right)-2\left(x^2-y^2\right)=\left(x-y\right)\left(x^2+y^2+xy\right)-2\left(x+y\right)\left(x-y\right)=\left(x-y\right)\left(x^2+y^2+xy-2\left(x+y\right)\right)\)8,
\(2x^3+3x^2-2x=x\left(2x^2+3x-2\right)=x\left(2x^2+4x-x-2\right)=x\left(2x\left(x+2\right)+\left(x+2\right)\right)=x\left(2x+1\right)\left(x+2\right)\)
9,
\(x^2-8x+7=x^2-x-7x+7=x\left(x-1\right)-7\left(x-1\right)=\left(x-7\right).\left(x-1\right)\)10,\(x^3-2x^2-8x=x\left(x^2-2x-8\right)=x\left(x^2+2x-4x-8\right)=x\left(x\left(x+2\right)-4\left(x+2\right)\right)=x\left(x-4\right)\left(x+2\right)\)
11,\(4x^2-5xy+y^2=4x^2-4xy-xy+y^2=4x\left(x-y\right)-y\left(x-y\right)=\left(x-y\right)\left(4x-y\right)\)12,
\(x^2-35y^2-2xy=x^2-7xy+5xy-35y^2=x\left(x-7y\right)+5y\left(x-7y\right)=\left(x-7y\right)\left(x+5y\right)\)13,
\(\left(x+y\right)^3-\left(x-y\right)^3=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x^3-3x^2y+3xy^2-y^3\right)=6x^2y+2y^3=2y\left(3x^2+y^2\right)\)
