展开 (x_{0}+ex_{1}+x_{2}e^2)^3

解答

展开

(x_{0} + e x_{1} + x_{2} e^{2})^{3}

x_{0}^{3} + 3 e x_{0}^{2} x_{1} + 3 e^{2} x_{0}^{2} x_{2} + 3 e^{2} x_{0} x_{1}^{2} + 3 e^{4} x_{0} x_{2}^{2} + 6 e^{3} x_{0} x_{1} x_{2} + e^{3} x_{1}^{3} + e^{6} x_{2}^{3} + 3 e^{5} x_{1} x_{2}^{2} + 3 e^{4} x_{1}^{2} x_{2}

求解步骤

(x_{0} + e x_{1} + x_{2} e^{2})^{3}

= (x_{0} + e x_{1} + e^{2} x_{2})^{3}

(x_{0} + e x_{1} + x_{2} e^{2})^{3} = (x_{0} + e x_{1} + x_{2} e^{2}) (x_{0} + e x_{1} + x_{2} e^{2}) (x_{0} + e x_{1} + x_{2} e^{2})

= (x_{0} + e x_{1} + e^{2} x_{2}) (x_{0} + e x_{1} + e^{2} x_{2}) (x_{0} + e x_{1} + e^{2} x_{2})

乘开

(x_{0} + e x_{1} + x_{2} e^{2}) (x_{0} + e x_{1} + x_{2} e^{2}) (x_{0} + e x_{1} + x_{2} e^{2}) : x_{0}^{3} + 3 e x_{0}^{2} x_{1} + 3 e^{2} x_{0}^{2} x_{2} + 3 e^{2} x_{0} x_{1}^{2} + 3 e^{4} x_{0} x_{2}^{2} + 6 e^{3} x_{0} x_{1} x_{2} + e^{3} x_{1}^{3} + e^{6} x_{2}^{3} + 3 e^{5} x_{1} x_{2}^{2} + 3 e^{4} x_{1}^{2} x_{2}

= x_{0}^{3} + 3 e x_{0}^{2} x_{1} + 3 e^{2} x_{0}^{2} x_{2} + 3 e^{2} x_{0} x_{1}^{2} + 3 e^{4} x_{0} x_{2}^{2} + 6 e^{3} x_{0} x_{1} x_{2} + e^{3} x_{1}^{3} + e^{6} x_{2}^{3} + 3 e^{5} x_{1} x_{2}^{2} + 3 e^{4} x_{1}^{2} x_{2}

\frac{d}{d x} ((z) (2 x^{2} + 3 y^{2} + 5 z^{2} - 9))

e x p an d e^{z} (z + 1)

e x p an d \frac{x - 8}{( x + 2 ) ( x ^{2} - 4 )}

e x p an d ln (x) (x ln (x) - x)

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