erweitern-xyz(x+y+z)^3

Lösung

erweitern

- x yz (x + y + z)^{3}

- x^{4} yz - 3 x^{3} y^{2} z - 3 x^{3} y z^{2} - 3 x^{2} y^{3} z - 3 x^{2} y z^{3} - 6 x^{2} y^{2} z^{2} - x y^{4} z - x y z^{4} - 3 x y^{2} z^{3} - 3 x y^{3} z^{2}

Schritte zur Lösung

- x yz (x + y + z)^{3}

(x + y + z)^{3} = x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x y^{2} + 3 x z^{2} + 6 x yz + y^{3} + z^{3} + 3 y z^{2} + 3 y^{2} z

= - x yz (x^{3} + 3 x^{2} y + 3 x^{2} z + 3 x y^{2} + 3 x z^{2} + 6 x yz + y^{3} + 3 y^{2} z + 3 y z^{2} + z^{3})

Setze Klammern

= (- x yz) x^{3} + (- x yz) \cdot 3 x^{2} y + (- x yz) \cdot 3 x^{2} z + (- x yz) \cdot 3 x y^{2} + (- x yz) \cdot 3 x z^{2} + (- x yz) \cdot 6 x yz + (- x yz) y^{3} + (- x yz) z^{3} + (- x yz) \cdot 3 y z^{2} + (- x yz) \cdot 3 y^{2} z

Wende Minus-Plus Regeln an

+ (- a) = - a

= - x^{3} x yz - 3 x^{2} x yyz - 3 x^{2} x yzz - 3 xx y^{2} yz - 3 xx y z^{2} z - 6 xx yyzz - x y^{3} yz - x y z^{3} z - 3 x yy z^{2} z - 3 x y^{2} yzz

Vereinfache

- x^{3} x yz - 3 x^{2} x yyz - 3 x^{2} x yzz - 3 xx y^{2} yz - 3 xx y z^{2} z - 6 xx yyzz - x y^{3} yz - x y z^{3} z - 3 x yy z^{2} z - 3 x y^{2} yzz : - x^{4} yz - 3 x^{3} y^{2} z - 3 x^{3} y z^{2} - 3 x^{2} y^{3} z - 3 x^{2} y z^{3} - 6 x^{2} y^{2} z^{2} - x y^{4} z - x y z^{4} - 3 x y^{2} z^{3} - 3 x y^{3} z^{2}

= - x^{4} yz - 3 x^{3} y^{2} z - 3 x^{3} y z^{2} - 3 x^{2} y^{3} z - 3 x^{2} y z^{3} - 6 x^{2} y^{2} z^{2} - x y^{4} z - x y z^{4} - 3 x y^{2} z^{3} - 3 x y^{3} z^{2}

e x p an d f (x - 3) +!

e x p an d (e + f)^{2} - g^{2}

e x p an d \frac{( - 4 - b ) i + 2 - 2 b}{5}

e x p an d \frac{( y )}{( 2 a - 1 ) ( 4 a - 5 )}

e x p an d (2 x^{2} y^{3} + 3 y^{5} - 20 y^{3}) d x