展开 9(9/n x+1)^3

解答

展开

9 (\frac{9}{n} x + 1)^{3}

\frac{9 ( 729 x ^{3} + 27 x n ^{2} + 243 n x ^{2} + n ^{3} )}{n ^{3}}

求解步骤

9 (\frac{9}{n} x + 1)^{3}

使用完全立方公式:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(\frac{9}{n} x + 1)^{3} = (\frac{9}{n} x)^{3} + 3 (\frac{9}{n} x)^{2} \cdot 1 + 3 \cdot \frac{9}{n} x \cdot 1^{2} + 1^{3}

= 9 ((\frac{9}{n} x)^{3} + 3 (\frac{9}{n} x)^{2} \cdot 1 + 3 \cdot \frac{9}{n} x \cdot 1^{2} + 1^{3})

化简

(\frac{9}{n} x)^{3} + 3 (\frac{9}{n} x)^{2} \cdot 1 + 3 \cdot \frac{9}{n} x \cdot 1^{2} + 1^{3} : \frac{729 x ^{3} + 27 x n ^{2} + 243 n x ^{2} + n ^{3}}{n ^{3}}

= 9 \cdot \frac{729 x ^{3} + 27 x n ^{2} + 243 n x ^{2} + n ^{3}}{n ^{3}}

使用分式法则:

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

= \frac{9 ( 729 x ^{3} + 27 x n ^{2} + 243 n x ^{2} + n ^{3} )}{n ^{3}}

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