展开 ((2x+5)^4)/8

解答

展开

\frac{( 2 x + 5 ) ^{4}}{8}

2 x^{4} + 20 x^{3} + 75 x^{2} + 125 x + \frac{625}{8}

求解步骤

\frac{( 2 x + 5 ) ^{4}}{8}

(2 x + 5)^{4} = 16 x^{4} + 160 x^{3} + 600 x^{2} + 1000 x + 625

= \frac{16 x ^{4} + 160 x ^{3} + 600 x ^{2} + 1000 x + 625}{8}

使用分式法则:

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

\frac{16 x ^{4} + 160 x ^{3} + 600 x ^{2} + 1000 x + 625}{8} = \frac{16 x ^{4}}{8} + \frac{160 x ^{3}}{8} + \frac{600 x ^{2}}{8} + \frac{1000 x}{8} + \frac{625}{8}

= \frac{16 x ^{4}}{8} + \frac{160 x ^{3}}{8} + \frac{600 x ^{2}}{8} + \frac{1000 x}{8} + \frac{625}{8}

\frac{16 x ^{4}}{8} = 2 x^{4}

\frac{160 x ^{3}}{8} = 20 x^{3}

\frac{600 x ^{2}}{8} = 75 x^{2}

\frac{1000 x}{8} = 125 x

= 2 x^{4} + 20 x^{3} + 75 x^{2} + 125 x + \frac{625}{8}

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