展开 ((1+2sqrt(x))^4)/8

解答

展开

\frac{( 1 + 2 x ) ^{4}}{8}

\frac{1}{8} + x + 3 x + 4 x^{\frac{3}{2}} + 2 x^{2}

求解步骤

\frac{( 1 + 2 x ) ^{4}}{8}

(1 + 2 x)^{4} = 1 + 8 x + 24 x + 32 x^{\frac{3}{2}} + 16 x^{2}

= \frac{1 + 8 x + 24 x + 32 x ^{\frac{3}{2}} + 16 x ^{2}}{8}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 + 8 x + 24 x + 32 x ^{\frac{3}{2}} + 16 x ^{2}}{8} = \frac{1}{8} + \frac{8 x}{8} + \frac{24 x}{8} + \frac{32 x ^{\frac{3}{2}}}{8} + \frac{16 x ^{2}}{8}

= \frac{1}{8} + \frac{8 x}{8} + \frac{24 x}{8} + \frac{32 x ^{\frac{3}{2}}}{8} + \frac{16 x ^{2}}{8}

\frac{8 x}{8} = x

\frac{24 x}{8} = 3 x

\frac{32 x ^{\frac{3}{2}}}{8} = 4 x^{\frac{3}{2}}

\frac{16 x ^{2}}{8} = 2 x^{2}

= \frac{1}{8} + x + 3 x + 4 x^{\frac{3}{2}} + 2 x^{2}

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