erweitern (x+y-3z)^5

Lösung

erweitern

(x + y - 3 z)^{5}

x^{5} + 5 x^{4} y - 15 x^{4} z + 10 x^{3} y^{2} + 90 x^{3} z^{2} - 60 x^{3} yz + 10 x^{2} y^{3} - 270 x^{2} z^{3} + 270 x^{2} y z^{2} - 90 x^{2} y^{2} z + 5 x y^{4} + 405 x z^{4} - 540 x y z^{3} + 270 x y^{2} z^{2} - 60 x y^{3} z + y^{5} - 243 z^{5} + 405 y z^{4} - 270 y^{2} z^{3} + 90 y^{3} z^{2} - 15 y^{4} z

Schritte zur Lösung

(x + y - 3 z)^{5}

(x + y - 3 z)^{5} = (x + y - 3 z) (x + y - 3 z) (x + y - 3 z) (x + y - 3 z) (x + y - 3 z)

= (x + y - 3 z) (x + y - 3 z) (x + y - 3 z) (x + y - 3 z) (x + y - 3 z)

Multipliziere aus

(x + y - 3 z) (x + y - 3 z) (x + y - 3 z) (x + y - 3 z) (x + y - 3 z) : x^{5} + 5 x^{4} y - 15 x^{4} z + 10 x^{3} y^{2} + 90 x^{3} z^{2} - 60 x^{3} yz + 10 x^{2} y^{3} - 270 x^{2} z^{3} + 270 x^{2} y z^{2} - 90 x^{2} y^{2} z + 5 x y^{4} + 405 x z^{4} - 540 x y z^{3} + 270 x y^{2} z^{2} - 60 x y^{3} z + y^{5} - 243 z^{5} + 405 y z^{4} - 270 y^{2} z^{3} + 90 y^{3} z^{2} - 15 y^{4} z

= x^{5} + 5 x^{4} y - 15 x^{4} z + 10 x^{3} y^{2} + 90 x^{3} z^{2} - 60 x^{3} yz + 10 x^{2} y^{3} - 270 x^{2} z^{3} + 270 x^{2} y z^{2} - 90 x^{2} y^{2} z + 5 x y^{4} + 405 x z^{4} - 540 x y z^{3} + 270 x y^{2} z^{2} - 60 x y^{3} z + y^{5} - 243 z^{5} + 405 y z^{4} - 270 y^{2} z^{3} + 90 y^{3} z^{2} - 15 y^{4} z

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

e x p an d n o t ab l es (x - 5)^{3}

e x p an d 9 (e - 4)

e x p an d 9 (h + 8 e)

e x p an d e^{c} (e^{x} x - e^{x}) + c