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受欢迎的代数 >

展开-((1-x^2)^4)/4

解答

展开

- \frac{( 1 - x ^{2} ) ^{4}}{4}

解答

- \frac{x ^{8}}{4} + x^{6} - \frac{3 x ^{4}}{2} + x^{2} - \frac{1}{4}

求解步骤

- \frac{( 1 - x ^{2} ) ^{4}}{4}

(1 - x^{2})^{4} = 1 - 4 x^{2} + 6 x^{4} - 4 x^{6} + x^{8}

= - \frac{x ^{8} - 4 x ^{6} + 6 x ^{4} - 4 x ^{2} + 1}{4}

使用分式法则:

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

\frac{1 - 4 x ^{2} + 6 x ^{4} - 4 x ^{6} + x ^{8}}{4} = - (\frac{1}{4}) - (- \frac{4 x ^{2}}{4}) - (\frac{6 x ^{4}}{4}) - (- \frac{4 x ^{6}}{4}) - (\frac{x ^{8}}{4})

= - (\frac{1}{4}) - (- \frac{4 x ^{2}}{4}) - (\frac{6 x ^{4}}{4}) - (- \frac{4 x ^{6}}{4}) - (\frac{x ^{8}}{4})

去除括号:

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

= - \frac{1}{4} + \frac{4 x ^{2}}{4} - \frac{6 x ^{4}}{4} + \frac{4 x ^{6}}{4} - \frac{x ^{8}}{4}

数字相除:

\frac{4}{4} = 1

= - \frac{1}{4} + x^{2} - \frac{6 x ^{4}}{4} + \frac{4 x ^{6}}{4} - \frac{x ^{8}}{4}

消掉

\frac{6 x ^{4}}{4} : \frac{3 x ^{4}}{2}

= - \frac{1}{4} + x^{2} - \frac{3 x ^{4}}{2} + \frac{4 x ^{6}}{4} - \frac{x ^{8}}{4}

数字相除:

\frac{4}{4} = 1

= - \frac{1}{4} + x^{2} - \frac{3 x ^{4}}{2} + x^{6} - \frac{x ^{8}}{4}

改写为标准形式

= - \frac{x ^{8}}{4} + x^{6} - \frac{3 x ^{4}}{2} + x^{2} - \frac{1}{4}

流行的例子

展开 (10x+4)dx

e x p an d (10 x + 4) d x

展开 (X(1-X)^3)/3

e x p an d \frac{X ( 1 - X ) ^{3}}{3}

e x p an d 133 \cdot 24

展开-((t^2+t)x+6x)/2

e x p an d - \frac{( t ^{2} + t ) x + 6 x}{2}

展开 ac(er+f)+ad+b

e x p an d a c (er + f) + a d + b