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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Multipliziere aus

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

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

e x p an d 3 (ln (9 x) + 1)

e x p an d 10 (a - 5 = 6 (a - 3))

e x p an d \frac{7 x ( 4 x + 7 )}{( 7 x - 4 ) ^{2}}

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

e x p an d 12 \cdot 4 \frac{1}{2}