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受欢迎的代数 >

展开-((7-x)^4)/4

解答

展开

- \frac{( 7 - x ) ^{4}}{4}

解答

- \frac{x ^{4}}{4} + 7 x^{3} - \frac{147 x ^{2}}{2} + 343 x - \frac{2401}{4}

求解步骤

- \frac{( 7 - x ) ^{4}}{4}

(7 - x)^{4} = 2401 - 1372 x + 294 x^{2} - 28 x^{3} + x^{4}

= - \frac{x ^{4} - 28 x ^{3} + 294 x ^{2} - 1372 x + 2401}{4}

使用分式法则:

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

\frac{2401 - 1372 x + 294 x ^{2} - 28 x ^{3} + x ^{4}}{4} = - (\frac{2401}{4}) - (- \frac{1372 x}{4}) - (\frac{294 x ^{2}}{4}) - (- \frac{28 x ^{3}}{4}) - (\frac{x ^{4}}{4})

= - (\frac{2401}{4}) - (- \frac{1372 x}{4}) - (\frac{294 x ^{2}}{4}) - (- \frac{28 x ^{3}}{4}) - (\frac{x ^{4}}{4})

去除括号:

(a) = a, - (- a) = a

= - \frac{2401}{4} + \frac{1372 x}{4} - \frac{294 x ^{2}}{4} + \frac{28 x ^{3}}{4} - \frac{x ^{4}}{4}

数字相除:

\frac{1372}{4} = 343

= - \frac{2401}{4} + 343 x - \frac{294 x ^{2}}{4} + \frac{28 x ^{3}}{4} - \frac{x ^{4}}{4}

消掉

\frac{294 x ^{2}}{4} : \frac{147 x ^{2}}{2}

= - \frac{2401}{4} + 343 x - \frac{147 x ^{2}}{2} + \frac{28 x ^{3}}{4} - \frac{x ^{4}}{4}

数字相除:

\frac{28}{4} = 7

= - \frac{2401}{4} + 343 x - \frac{147 x ^{2}}{2} + 7 x^{3} - \frac{x ^{4}}{4}

改写为标准形式

= - \frac{x ^{4}}{4} + 7 x^{3} - \frac{147 x ^{2}}{2} + 343 x - \frac{2401}{4}

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