Question

Phân tích đa thức thành nhân tử:x²y + xy² + x²z + xz² + y²z + yz² +3xyz

Answer 1

x²y + xy² + x²z + xz² + y²z + yz² +3xyz

=(x²y+x²z)+(xy²+xz²)+(y²z+yz²)+3xyz

=x²(y+z)+x(y²+z²)+yz(y+z)+2xyz+xyz

=x²(y+z)+x(y²+z²+2yz)+yz(y+z+x)

=(y+z)x(x+y+z)+yz(y+x+z)

=(x+y+z)(xy+xz+yz)

Answer 2

x²y + xy² + x²z + xz² + y²z + yz² + 3xyz

=(x²y + xy² + xyz) + (x²z + xyz + xz²) + (xyz + y²z + yz²)

=xy(x + y + z) + xz(x + y + z) + yz(x + y +z)

=(x + y + z)(xy + xz + yz)