erweitern (x+2y+3z)^5

Lösung

erweitern

(x + 2 y + 3 z)^{5}

x^{5} + 10 x^{4} y + 15 x^{4} z + 40 x^{3} y^{2} + 90 x^{3} z^{2} + 120 x^{3} yz + 80 x^{2} y^{3} + 270 x^{2} z^{3} + 540 x^{2} y z^{2} + 360 x^{2} y^{2} z + 80 x y^{4} + 405 x z^{4} + 1080 x y z^{3} + 1080 x y^{2} z^{2} + 480 x y^{3} z + 32 y^{5} + 243 z^{5} + 810 y z^{4} + 1080 y^{2} z^{3} + 720 y^{3} z^{2} + 240 y^{4} z

Schritte zur Lösung

(x + 2 y + 3 z)^{5}

(x + 2 y + 3 z)^{5} = (x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z)

= (x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z)

Multipliziere aus

(x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z) (x + 2 y + 3 z) : x^{5} + 10 x^{4} y + 15 x^{4} z + 40 x^{3} y^{2} + 90 x^{3} z^{2} + 120 x^{3} yz + 80 x^{2} y^{3} + 270 x^{2} z^{3} + 540 x^{2} y z^{2} + 360 x^{2} y^{2} z + 80 x y^{4} + 405 x z^{4} + 1080 x y z^{3} + 1080 x y^{2} z^{2} + 480 x y^{3} z + 32 y^{5} + 243 z^{5} + 810 y z^{4} + 1080 y^{2} z^{3} + 720 y^{3} z^{2} + 240 y^{4} z

= x^{5} + 10 x^{4} y + 15 x^{4} z + 40 x^{3} y^{2} + 90 x^{3} z^{2} + 120 x^{3} yz + 80 x^{2} y^{3} + 270 x^{2} z^{3} + 540 x^{2} y z^{2} + 360 x^{2} y^{2} z + 80 x y^{4} + 405 x z^{4} + 1080 x y z^{3} + 1080 x y^{2} z^{2} + 480 x y^{3} z + 32 y^{5} + 243 z^{5} + 810 y z^{4} + 1080 y^{2} z^{3} + 720 y^{3} z^{2} + 240 y^{4} z

e x p an d 2 (6 + ln (\frac{53}{2}))

\frac{d}{d x} ((x) (2 x^{2} y + 4))

e x p an d x + 2 \cdot (3 x - 2)

e x p an d 25 t (1 + e^{2 t})

e x p an d \frac{3 x ^{2} + 5}{x ^{2} ( x ^{2} + x + 1 ) ^{2}}