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受欢迎的代数 >

展开-1/12 (x)(((96-16x))/(12))^3

解答

展开

- \frac{1}{12} (x) (\frac{( 96 - 16 x )}{12})^{3}

解答

\frac{16 x ^{4}}{81} - \frac{32 x ^{3}}{9} + \frac{64 x ^{2}}{3} - \frac{128 x}{3}

求解步骤

- \frac{1}{12} (x) (\frac{96 - 16 x}{12})^{3}

去除括号:

(a) = a

= - \frac{1}{12} x (\frac{96 - 16 x}{12})^{3}

(\frac{96 - 16 x}{12})^{3} = \frac{- 64 x ^{3} + 1152 x ^{2} - 6912 x + 13824}{3 ^{3}}

= - \frac{1}{12} \cdot \frac{- 64 x ^{3} + 1152 x ^{2} - 6912 x + 13824}{3 ^{3}} x

分式相乘:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= - \frac{1 \cdot ( - 64 x ^{3} + 1152 x ^{2} - 6912 x + 13824 ) x}{12 \cdot 3 ^{3}}

乘以:

1 \cdot (- 64 x^{3} + 1152 x^{2} - 6912 x + 13824) = (- 64 x^{3} + 1152 x^{2} - 6912 x + 13824)

= - \frac{x ( - 64 x ^{3} + 1152 x ^{2} - 6912 x + 13824 )}{3 ^{3} \cdot 12}

消掉

\frac{( - 64 x ^{3} + 1152 x ^{2} - 6912 x + 13824 ) x}{12 \cdot 3 ^{3}} : \frac{16 x ( - x ^{3} + 18 x ^{2} - 108 x + 216 )}{3 ^{3} \cdot 3}

= - \frac{16 x ( - x ^{3} + 18 x ^{2} - 108 x + 216 )}{3 ^{3} \cdot 3}

3^{3} \cdot 3 = 3^{4}

= - \frac{16 x ( - x ^{3} + 18 x ^{2} - 108 x + 216 )}{3 ^{4}}

3^{4} = 81

= - \frac{16 x ( - x ^{3} + 18 x ^{2} - 108 x + 216 )}{81}

乘开

16 x (- x^{3} + 18 x^{2} - 108 x + 216) : - 16 x^{4} + 288 x^{3} - 1728 x^{2} + 3456 x

= - \frac{- 16 x ^{4} + 288 x ^{3} - 1728 x ^{2} + 3456 x}{81}

使用分式法则:

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

\frac{- 16 x ^{4} + 288 x ^{3} - 1728 x ^{2} + 3456 x}{81} = - (- \frac{16 x ^{4}}{81}) - (\frac{288 x ^{3}}{81}) - (- \frac{1728 x ^{2}}{81}) - (\frac{3456 x}{81})

= - (- \frac{16 x ^{4}}{81}) - (\frac{288 x ^{3}}{81}) - (- \frac{1728 x ^{2}}{81}) - (\frac{3456 x}{81})

去除括号:

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

= \frac{16 x ^{4}}{81} - \frac{288 x ^{3}}{81} + \frac{1728 x ^{2}}{81} - \frac{3456 x}{81}

消掉

\frac{288 x ^{3}}{81} : \frac{32 x ^{3}}{9}

= \frac{16 x ^{4}}{81} - \frac{32 x ^{3}}{9} + \frac{1728 x ^{2}}{81} - \frac{3456 x}{81}

消掉

\frac{1728 x ^{2}}{81} : \frac{64 x ^{2}}{3}

= \frac{16 x ^{4}}{81} - \frac{32 x ^{3}}{9} + \frac{64 x ^{2}}{3} - \frac{3456 x}{81}

消掉

\frac{3456 x}{81} : \frac{128 x}{3}

= \frac{16 x ^{4}}{81} - \frac{32 x ^{3}}{9} + \frac{64 x ^{2}}{3} - \frac{128 x}{3}

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