展开 (x+2y+3z)^5

解答

展开

(x + 2 \cdot y + 3 \cdot 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

求解步骤

(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)

乘开

(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 \frac{( x + 2 ) ( x - 4 )}{( x + 5 ) ( x - 3 )}

e x p an d \frac{π ^{2}}{6} (x - \frac{1}{2})

e x p an d (x^{2} + x y + y^{2})^{6}

e x p an d (3 - \frac{3}{2} y) 3

e x p an d cos (x y) (y + x \frac{d y}{d x})