展开 (x+y+z)^5

解答

展开

(x + y + z)^{5}

x^{5} + 5 x^{4} y + 5 x^{4} z + 10 x^{3} y^{2} + 10 x^{3} z^{2} + 20 x^{3} yz + 10 x^{2} y^{3} + 10 x^{2} z^{3} + 30 x^{2} y z^{2} + 30 x^{2} y^{2} z + 5 x y^{4} + 5 x z^{4} + 20 x y z^{3} + 30 x y^{2} z^{2} + 20 x y^{3} z + y^{5} + z^{5} + 5 y z^{4} + 10 y^{2} z^{3} + 10 y^{3} z^{2} + 5 y^{4} z

求解步骤

(x + y + z)^{5}

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

= (x + y + z) (x + y + z) (x + y + z) (x + y + z) (x + y + z)

乘开

(x + y + z) (x + y + z) (x + y + z) (x + y + z) (x + y + z) : x^{5} + 5 x^{4} y + 5 x^{4} z + 10 x^{3} y^{2} + 10 x^{3} z^{2} + 20 x^{3} yz + 10 x^{2} y^{3} + 10 x^{2} z^{3} + 30 x^{2} y z^{2} + 30 x^{2} y^{2} z + 5 x y^{4} + 5 x z^{4} + 20 x y z^{3} + 30 x y^{2} z^{2} + 20 x y^{3} z + y^{5} + z^{5} + 5 y z^{4} + 10 y^{2} z^{3} + 10 y^{3} z^{2} + 5 y^{4} z

= x^{5} + 5 x^{4} y + 5 x^{4} z + 10 x^{3} y^{2} + 10 x^{3} z^{2} + 20 x^{3} yz + 10 x^{2} y^{3} + 10 x^{2} z^{3} + 30 x^{2} y z^{2} + 30 x^{2} y^{2} z + 5 x y^{4} + 5 x z^{4} + 20 x y z^{3} + 30 x y^{2} z^{2} + 20 x y^{3} z + y^{5} + z^{5} + 5 y z^{4} + 10 y^{2} z^{3} + 10 y^{3} z^{2} + 5 y^{4} z

e x p an d 3 (x + 2 = 5)

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

s im pl i f y (x + 3)^{2}

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

e x p an d ln (ab)