Question

1) x³-x²y-xy²+y³

2) 3x+3y-x²-2xy-y²

Answer 1

1)

\(=\left(x^3+y^3\right)-\left(x^2y+xy^2\right)=\left(x+y\right)\left(x^2-xy+y^2\right)-xy\left(x+y\right)=\left(x+y\right)\left(x^2-2xy+y^2\right)=\left(x+y\right)\left(x-y\right)^2\)

2)

\(=3\left(x+y\right)-\left(x+y\right)^2=\left(x+y\right)\left(3-x+y\right)\)

Answer 2

1)\(x^3\)-\(x^2\)y-x\(y^2\)+y^3=x^2(x-y)-y^2(x-y)=(x-y)(x^2-y^2)=(x-y)(x-y)(x+y)

2)3x+3y-x^2-2xy-y^2=(3x+3y)-(x^2+2xy+y^2)=3(x+y)-(x+y)^2=(x+y)(3-x+y)