Question

Ma ajuta cineva sa demonstrez formula
$(x+y+z) ^{2}$

Answer 1

[tex](x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx\\ Demonstraie:\\ (x+y+z)^2=(x+y+z)(x+y+z)\\ Inmutlim~fiecare~termen~din ~prima~paranteza~cu ~fiecare~termen~\\din~cea~de-a~doua~paranteza:\\ ...=x^2+xy+xz+yx+y^2+yz+zx+zy+z^2=\\=x^2+y^2+z^2+xy+yx+zy+yz+xz+zx=\\=x^2+y^2+z^2+2xy+2yz+2zx.[/tex]