展开 ((3x+1)^3)/3

解答

展开

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

9 x^{3} + 9 x^{2} + 3 x + \frac{1}{3}

求解步骤

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

(3 x + 1)^{3} = 27 x^{3} + 27 x^{2} + 9 x + 1

= \frac{27 x ^{3} + 27 x ^{2} + 9 x + 1}{3}

使用分式法则:

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

\frac{27 x ^{3} + 27 x ^{2} + 9 x + 1}{3} = \frac{27 x ^{3}}{3} + \frac{27 x ^{2}}{3} + \frac{9 x}{3} + \frac{1}{3}

= \frac{27 x ^{3}}{3} + \frac{27 x ^{2}}{3} + \frac{9 x}{3} + \frac{1}{3}

数字相除:

\frac{27}{3} = 9

= 9 x^{3} + 9 x^{2} + \frac{9 x}{3} + \frac{1}{3}

数字相除:

\frac{9}{3} = 3

= 9 x^{3} + 9 x^{2} + 3 x + \frac{1}{3}

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