Question

Разложите на множители x(y^2 −z^2)+y(z^2 −x^2)+z(x^2 −y^2).

Answer 1

x(y² - z²) + y(z² - x²) + z(x² - y²) = xy² - x²y + x²z - y²z + yz² - xz² =

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

= y(xy - x² + xz - yz) + z(x² + yz - xy - xz) =

= y(xy - x² + xz - yz) - z(xy - x² + xz - yz) = (y - z)(xy - x² + xz - yz) =

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