faktorisieren (x+y+z)(xy+xz+yz)-xyz

Lösung

faktorisieren

(x + y + z) (x y + x z + yz) - x yz

x^{2} y + x^{2} z + x y^{2} + x z^{2} + 2 x yz + y z^{2} + y^{2} z

Schritte zur Lösung

(x + y + z) (x y + x z + yz) - x yz

Multipliziere aus

(x + y + z) (x y + x z + yz) : x^{2} y + x y^{2} + x^{2} z + 3 x yz + x z^{2} + y^{2} z + y z^{2}

= x^{2} y + x y^{2} + x^{2} z + 3 x yz + x z^{2} + y^{2} z + y z^{2} - x yz

Vereinfache

x^{2} y + x y^{2} + x^{2} z + 3 x yz + x z^{2} + y^{2} z + y z^{2} - x yz : x^{2} y + x^{2} z + x y^{2} + x z^{2} + 2 x yz + y z^{2} + y^{2} z

= x^{2} y + x^{2} z + x y^{2} + x z^{2} + 2 x yz + y z^{2} + y^{2} z

f a c t or 63

f a c t or x y - b x + a y - ab

f a c t or (a - 1)^{2} + 3 (a - 1) - 108

f a c t or x^{2} - 10 + 25

s im pl i f y [- 3.6]