1) \(3y^2-9y=3y\left(y-3\right)\)
2) \(7x-7y+x^2-2xy+y^2\\ =7\left(x-y\right)+\left(x^2-2xy+y^2\right)\\ =7\left(x-y\right)+\left(x-y\right)^2\\ =\left(x-y\right)\left(7+x-y\right)\)
3)
\(x\left(x-y\right)+y\left(y-x\right)\\ =x\left(x-y\right)-y\left(x-y\right)\\ =\left(x-y\right)\left(x-y\right)\\ =\left(x-y\right)^2\)
4)
\(x^2-x-y^2-y\\ =\left(x^2-y^2\right)-\left(x+y\right)\\ =\left(x-y\right)\left(x+y\right)-\left(x+y\right)\\ =\left(x+y\right)\left(x-y-1\right)\)
5)
\(\left(x^2+xy\right)^2-\left(y^2+xy\right)^2\\ =\left(x^2+xy-y^2-xy\right)\left(x^2+xy+y^2+xy\right)\\ =\left(x^2-y^2\right)\left(x^2+2xy+y^2\right)\\ =\left(x-y\right)\left(x+y\right)\left(x+y\right)^2\\ =\left(x-y\right)\left(x+y\right)^3\)
6)
\(=3\left(x^2+2xy+y^2-z^2\right)\\ =3\left[\left(x+y\right)^2-z^2\right]\\ =3\left(x+y+z\right)\left(x+y-z\right)\)
7) (mik ko chắc)
\(=x^3-3x^2y+3xy^2-y^3+y^3-3y^2z+3yz^2-z^3+z^3-3z^2x+3zx^2-x^3\)
\(=3xy^2-3x^2y-3y^2z+3yz^2-3z^2x+3zx^2\)
\(=3\left(xy^2-x^2y-y^2z+yz^2-z^2x+zx^2\right)\)
8)
\(x^2-6x+5\\ =x^2-5x-x+5\\ =x\left(x-5\right)-\left(x-5\right)\\ =\left(x-5\right)\left(x-1\right)\)
9)
\(x^3+64\\ =\left(x+4\right)\left(x^2-4x+16\right)\)
10)
\(2x^2-3x-5\\ =2x^2-5x+2x-5\\ =x\left(2x-5\right)+\left(2x-5\right)\\ =\left(2x-5\right)\left(x+1\right)\)
