Question

ДАЮ 30 БАЛЛОВ!!!
x²(y-z)+y²(z-x)+z²(x-y)
Разложите на множители ​

Answer 1

Ответ: x²(y-z)+y²(z-x)+z²(x-y)= (x-y)(x-z)(y-z)

Объяснение: x²(y-z)+y²(z-x)+z²(x-y)=(x-y)(x-z)(y-z)

x²(y-z)+y²(z-x)+z²(x-y)=х²у-х²z+y²z+y²x+z²(x-y)=xy(x-y)-z(x²-y²)+z²(x-y)=(x-y)(xy-z(x+y)+z²)=(x-y)(xy-zx-zy+z²)=(x-y)(x(y-z)-z(y-z))=(x-y)(x-z)(y-z)