展开 (2+5x)((1-x)/2)^8

解答

展开

(2 + 5 x) (\frac{1 - x}{2})^{8}

\frac{( 1 - x ) ^{8}}{128} + \frac{5 ( 1 - x ) ^{8} x}{256}

求解步骤

(2 + 5 x) (\frac{1 - x}{2})^{8}

= (\frac{1 - x}{2})^{8} (2 + 5 x)

使用分配律:

a (b + c) = ab + a c

(\frac{1 - x}{2})^{8} (2 + 5 x) = (\frac{1 - x}{2})^{8} \cdot 2 + (\frac{1 - x}{2})^{8} \cdot 5 x

= (\frac{1 - x}{2})^{8} \cdot 2 + (\frac{1 - x}{2})^{8} \cdot 5 x

化简

(\frac{1 - x}{2})^{8} \cdot 2 + (\frac{1 - x}{2})^{8} \cdot 5 x : \frac{( 1 - x ) ^{8}}{128} + \frac{5 ( 1 - x ) ^{8} x}{256}

= \frac{( 1 - x ) ^{8}}{128} + \frac{5 ( 1 - x ) ^{8} x}{256}

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