erweitern (x+y+z+w+u)^3

Lösung

erweitern

(x + y + z + w + u)^{3}

x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x^{2} w + 3 x^{2} u + 3 x y^{2} + 3 x z^{2} + 6 x yz + 3 x w^{2} + 6 x y w + 6 x z w + 3 x u^{2} + 6 x y u + 6 x z u + 6 x w u + y^{3} + z^{3} + 3 y z^{2} + 3 y^{2} z + w^{3} + 3 y w^{2} + 3 z w^{2} + 3 y^{2} w + 6 yz w + 3 z^{2} w + u^{3} + 3 y u^{2} + 3 z u^{2} + 3 w u^{2} + 3 y^{2} u + 6 yz u + 3 z^{2} u + 6 y w u + 6 z w u + 3 w^{2} u

Schritte zur Lösung

(x + y + z + w + u)^{3}

(x + y + z + w + u)^{3} = (x + y + z + w + u) (x + y + z + w + u) (x + y + z + w + u)

= (x + y + z + w + u) (x + y + z + w + u) (x + y + z + w + u)

Multipliziere aus

(x + y + z + w + u) (x + y + z + w + u) (x + y + z + w + u) : x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x^{2} w + 3 x^{2} u + 3 x y^{2} + 3 x z^{2} + 6 x yz + 3 x w^{2} + 6 x y w + 6 x z w + 3 x u^{2} + 6 x y u + 6 x z u + 6 x w u + y^{3} + z^{3} + 3 y z^{2} + 3 y^{2} z + w^{3} + 3 y w^{2} + 3 z w^{2} + 3 y^{2} w + 6 yz w + 3 z^{2} w + u^{3} + 3 y u^{2} + 3 z u^{2} + 3 w u^{2} + 3 y^{2} u + 6 yz u + 3 z^{2} u + 6 y w u + 6 z w u + 3 w^{2} u

= x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x^{2} w + 3 x^{2} u + 3 x y^{2} + 3 x z^{2} + 6 x yz + 3 x w^{2} + 6 x y w + 6 x z w + 3 x u^{2} + 6 x y u + 6 x z u + 6 x w u + y^{3} + z^{3} + 3 y z^{2} + 3 y^{2} z + w^{3} + 3 y w^{2} + 3 z w^{2} + 3 y^{2} w + 6 yz w + 3 z^{2} w + u^{3} + 3 y u^{2} + 3 z u^{2} + 3 w u^{2} + 3 y^{2} u + 6 yz u + 3 z^{2} u + 6 y w u + 6 z w u + 3 w^{2} u

e x p an d 2 (x - 2 y = 10)

e x p an d 5 (5 x^{2} - 2 x + 1)^{2}

e x p an d \frac{( v - 1 ) ( v ^{2} + v + 1 )}{v ^{2}}

e x p an d (4 y^{2} - 24 y + 34) e^{- y^{2} + 6 y}

e x p an d \frac{( x + 1 ) ( x - 10 )}{80}