Question

HELP ME !!!

Phân tích đa thức thành nhân tử :

x (y² - z² ) + y ( z² - x² ) + z ( x² - y² )

Answer 1

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

=\(xy^2-xz^2+yz^2-x^2y+zx^2-zy^2\)

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

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

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

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

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

Answer 2

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

\(y^2z-z^3+yz^2-x^2y+x^2z-y^2z\)

\(-z^3yz^2-x^2y+x^2z\)