Question #10309

using factor theorem, show that x-y, y-z are the factors of x9x^2-z^2)+y(z^2-x^2)+z(x^2-y^2)

Expert's answer

x(x^2-z^2)+y(z^2-x^2)+z(x^2-y^2)=x(x-z)(x+z)+y(z-x)(z+x)+z(x-y)(x+y)=-x(z-x)(x+z)+y(z-x)(z+x)+z(x-y)(x+y)=(z-x)(z+x)(y-x)-z(y-x)(x+y)=

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

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

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