Question

scrieti ca produs de trei factori 
 a) xyz+xy+yz+zx+x+y+z+1
b)xyz-xy+yz-zx+x-y-z+1
c)abc-3ab-bc-2ac-6a+3b-2c+6

Answer 1

a)xyz+yz+zx+xxyz+xy+y+z+1 = xy(z+1)+y(z+1)+x(z+1)+(z+1 )
(z+1)(xy+y+x+1) = (z+1)[y(x+1)+(x+1)]= (z+1)(x+1)(y+1)

b)xyz-xy+yz-zx+x-y-z+1 =xy(z-1)+y(z-1)+x(z-1)=
(z-1)(xy+y+x+1)=(z-1)[y(x+1)+(x+1)]=(z-1)(x+1)(y+1)

c)abc-3ab-bc-2ac-6a+3b-2c+6 =abc-3ab-2ac-6a-bc+3b-2c+6
   ab(c-3) -2a(c-3)-b(c-3)-2(c-3) = (c-3)(ab-2a-b-2)= (c-3)[b(a-1)-2(a-1)]
=(c-1)(a-1)(b-2)