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受欢迎的代数 >

展开 ((4-x)(16+5x^2))/8

解答

展开

\frac{( 4 - x ) ( 16 + 5 x ^{2} )}{8}

解答

- \frac{5 x ^{3}}{8} + \frac{5 x ^{2}}{2} - 2 x + 8

求解步骤

\frac{( 4 - x ) ( 16 + 5 x ^{2} )}{8}

乘开

(4 - x) (16 + 5 x^{2}) : 64 + 20 x^{2} - 16 x - 5 x^{3}

= \frac{64 + 20 x ^{2} - 16 x - 5 x ^{3}}{8}

使用分式法则:

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

\frac{64 + 20 x ^{2} - 16 x - 5 x ^{3}}{8} = \frac{64}{8} + \frac{20 x ^{2}}{8} - \frac{16 x}{8} - \frac{5 x ^{3}}{8}

= \frac{64}{8} + \frac{20 x ^{2}}{8} - \frac{16 x}{8} - \frac{5 x ^{3}}{8}

数字相除:

\frac{64}{8} = 8

= 8 + \frac{20 x ^{2}}{8} - \frac{16 x}{8} - \frac{5 x ^{3}}{8}

消掉

\frac{20 x ^{2}}{8} : \frac{5 x ^{2}}{2}

= 8 + \frac{5 x ^{2}}{2} - \frac{16 x}{8} - \frac{5 x ^{3}}{8}

数字相除:

\frac{16}{8} = 2

= 8 + \frac{5 x ^{2}}{2} - 2 x - \frac{5 x ^{3}}{8}

改写为标准形式

= - \frac{5 x ^{3}}{8} + \frac{5 x ^{2}}{2} - 2 x + 8

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