Докажите тождество (y^4+y^3)(y^2-y)=y^3(y62+1)(y-1)

[latex](y^4+y^3)(y^2-y)=y^3(y^2+1)(y-1) \\ y^3(y+1)*y(y-1)-y^3(y^2+1)(y-1)=0 \\ y^4(y^2-1)-y^3(y^2+1)(y-1)=0 \\ y^4(y-1)(y+1)-y^3(y^2+1)(y-1)=0 \\ (y-1)y^3(y(y+1)-(y^2+1))=0 \\ (y-1)y^3(y^2+y-y^2-1=0 \\ y^3(y-1)(y-1)=0 \\ y^3(y-1)^2=0 \\ 1) y^3=0 y=0 2)(y-1)^2=0 y=1 [/latex]