a) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)

\(=x^2y+xy^2+xyz+x^2z+xz^2+xyz+y^2z+yz^2\)

\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z\right)\)

\(=\left(x+y+z\right)\left(xy+xz\right)+yz\left(y+z\right)\)

\(=x\left(x+y+z\right)\left(y+z\right)+yz\left(y+z\right)\)

\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)

\(=\left(y+z\right)\left[x\left(x+y\right)+z\left(x+y\right)\right]=\left(y+z\right)\left(x+y\right)\left(x+z\right)\)

b) \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2+xyz\right)\)

\(=xy\left(x+y+z\right)+xz\left(x+z+y\right)+yz\left(y+z+x\right)\)

\(=\left(x+y+z\right)\left(xy+xz+yz\right)\)

P/s: Sai sót xin bỏ qua.

       \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2+xyz\right)\)

\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(xy+xz+yz\right)\)

nick ko hay rồi tcn còn ko hay nữa

\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz.\)

\(=x^2.\left(y+z\right)+yz.\left(y+z\right)+x\left(y^2+z^3\right)+2xyz\)

\(=\left(y+z\right).\left(x^2+yz\right)+x\left(y^{^2}+z^2+2yz\right)\)

\(=\left(y+z\right).\left[x.\left(x+2\right)+y.\left(x+2\right)\right]\)

\(=\left(y+z\right).\left(x+z\right).\left(x+y\right)\)

Ta có: \(x^2y-xy^2+y^2z-yz^2+xz^2-x^2z=xy\left(x-y\right)-z\left(x^2-y^2\right)+z^2\left(x-y\right)\)

\(=xy\left(x-y\right)-z\left(x-y\right)\left(x+y\right)+z^2\left(x-y\right)=\left(x-y\right)\left(xy-zx-zy+z^2\right)\)

\(=\left(x-y\right)\left(x\left(y-z\right)-z\left(y-z\right)\right)=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)

b) Ta có: \(x^3-x^2y-xy^2+y^3\)

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

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

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

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

Bài 3:

a: =>(2x-7)(x-2)=0

=>x=7/2 hoặc x=2

b: =>(x-1)(x+2)=0

=>x=1 hoặc x=-2

d: =>2x+3=0

hay x=-3/2