展开 (1024l(c-2t-a)^2)/(405pid^4)

解答

展开

\frac{1024 l ( c - 2 t - a ) ^{2}}{405 π d ^{4}}

- \frac{4096 l c t}{405 π d ^{4}} + \frac{4096 l a t}{405 π d ^{4}} + \frac{4096 l t ^{2}}{405 π d ^{4}} + \frac{1024 l c ^{2}}{405 π d ^{4}} - \frac{2048 l c a}{405 π d ^{4}} + \frac{1024 l a ^{2}}{405 π d ^{4}}

求解步骤

\frac{1024 l ( c - 2 t - a ) ^{2}}{405 π d ^{4}}

(c - 2 t - a)^{2} = - 4 c t + 4 a t + 4 t^{2} + c^{2} - 2 c a + a^{2}

= \frac{1024 l ( 4 t ^{2} + 4 a t - 4 c t + c ^{2} + a ^{2} - 2 c a )}{405 π d ^{4}}

乘开

1024 l (- 4 c t + 4 a t + 4 t^{2} + c^{2} - 2 c a + a^{2}) : - 4096 l c t + 4096 l a t + 4096 l t^{2} + 1024 l c^{2} - 2048 l c a + 1024 l a^{2}

= \frac{- 4096 l c t + 4096 l a t + 4096 l t ^{2} + 1024 l c ^{2} - 2048 l c a + 1024 l a ^{2}}{405 π d ^{4}}

使用分式法则:

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

\frac{- 4096 l c t + 4096 l a t + 4096 l t ^{2} + 1024 l c ^{2} - 2048 l c a + 1024 l a ^{2}}{405 π d ^{4}} = - \frac{4096 l c t}{405 π d ^{4}} + \frac{4096 l a t}{405 π d ^{4}} + \frac{4096 l t ^{2}}{405 π d ^{4}} + \frac{1024 l c ^{2}}{405 π d ^{4}} - \frac{2048 l c a}{405 π d ^{4}} + \frac{1024 l a ^{2}}{405 π d ^{4}}

= - \frac{4096 l c t}{405 π d ^{4}} + \frac{4096 l a t}{405 π d ^{4}} + \frac{4096 l t ^{2}}{405 π d ^{4}} + \frac{1024 l c ^{2}}{405 π d ^{4}} - \frac{2048 l c a}{405 π d ^{4}} + \frac{1024 l a ^{2}}{405 π d ^{4}}

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