展开 (x+3y-2z)^5

解答

展开

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

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

求解步骤

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

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

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

乘开

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

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

e x p an d \frac{e ^{- 2 s}}{( s ^{2} + 1 ) ( s ^{2} + 9 )}

e x p an d \frac{s ^{2} + s + 16}{( s ^{2} + 16 ) ^{2}}

e x p an d e^{x^{6} e^{x}} \cdot (x - 4 y = x^{6} e^{x})

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

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