Question

phân tích đa thức thành nhân tử:

M = 3xyz + x ( y²+z²) + y ( x²+z²) + z ( x²+y²)

Answer 1

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

\(M=3xyz+xy^2+xz^2+yx^2+yz^2+zx^2+zy^2\)

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

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