Question

因式分解x平方y+y平方z+z平方x-x平方z-y平方x-z平方y

Answer 1

x²y+y²z+z²x-x²z-y²x-z²y

=(x²y-x²z)+(y²z-z²y)+(z²x-y²x)

=x²(y-z)+yz(y-z)+x(z-y)(z+y)

=(y-z)(x²+yz-xz-xy)

=(y-z)[x(x-z)+y(z-x)]

=(y-z)(x-z)(x-y)