Разложить на множители:x(y - z) + y(z - x) + z(x

Ответ:

Изъясненье:

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

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

a + b + c - 3abc = a + ab + ac - ab - ab - abc - ac - abc - ac +

+ ab + bc - bc - bc + ac + bc = a(a + b + c) - ab(a + b + c) -

- ac(a + b + c) + b(a + b + c) - bc(a + b + c) + c(a + b + c) =

= (a + b + c)(a - ab - ac + b - bc + c).