展开 ((x+7)^7)/8

解答

展开

\frac{( x + 7 ) ^{7}}{8}

\frac{x ^{7}}{8} + \frac{49 x ^{6}}{8} + \frac{1029 x ^{5}}{8} + \frac{12005 x ^{4}}{8} + \frac{84035 x ^{3}}{8} + \frac{352947 x ^{2}}{8} + \frac{823543 x}{8} + \frac{823543}{8}

求解步骤

\frac{( x + 7 ) ^{7}}{8}

(x + 7)^{7} = x^{7} + 49 x^{6} + 1029 x^{5} + 12005 x^{4} + 84035 x^{3} + 352947 x^{2} + 823543 x + 823543

= \frac{x ^{7} + 49 x ^{6} + 1029 x ^{5} + 12005 x ^{4} + 84035 x ^{3} + 352947 x ^{2} + 823543 x + 823543}{8}

使用分式法则:

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

\frac{x ^{7} + 49 x ^{6} + 1029 x ^{5} + 12005 x ^{4} + 84035 x ^{3} + 352947 x ^{2} + 823543 x + 823543}{8} = \frac{x ^{7}}{8} + \frac{49 x ^{6}}{8} + \frac{1029 x ^{5}}{8} + \frac{12005 x ^{4}}{8} + \frac{84035 x ^{3}}{8} + \frac{352947 x ^{2}}{8} + \frac{823543 x}{8} + \frac{823543}{8}

= \frac{x ^{7}}{8} + \frac{49 x ^{6}}{8} + \frac{1029 x ^{5}}{8} + \frac{12005 x ^{4}}{8} + \frac{84035 x ^{3}}{8} + \frac{352947 x ^{2}}{8} + \frac{823543 x}{8} + \frac{823543}{8}

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