Question

Разложите на множители:
1) x(y+z)^2+y(x+z)^2+z(x+y)^2-4xyz
2) (ab+ac+bc)(a+b+c)-abc 

Answer 1

$x(y+z)^2+y(x+z)^2+z(x+y)^2-4xyz=\=x(y^2+2yz+z^2)+y(x^2+2xz+z^2)+z(x^2+2xy+y^2)-4xyz=\=xy^2+2xyz+\+xz^2+yx^2+2xyz+yz^2+zx^2+2xyz+zy^2=\=xy^2+yx^2+zx^2+zy^2+xz^2+yz^2+2xyz=\=xyzleft(cfrac{y}{z}+cfrac{x}{z}+cfrac{x}{y}+cfrac{y}{x}+cfrac{z}{y}+cfrac{z}{x}right)+2xyz=\=(xyz+2)left(cfrac{y}{z}+cfrac{x}{z}+cfrac{x}{y}+cfrac{y}{x}+cfrac{z}{y}+cfrac{z}{x}right)$