展开 ((2x+3)^3)/6

解答

展开

\frac{( 2 x + 3 ) ^{3}}{6}

\frac{4 x ^{3}}{3} + 6 x^{2} + 9 x + \frac{9}{2}

求解步骤

\frac{( 2 x + 3 ) ^{3}}{6}

(2 x + 3)^{3} = 8 x^{3} + 36 x^{2} + 54 x + 27

= \frac{8 x ^{3} + 36 x ^{2} + 54 x + 27}{6}

使用分式法则:

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

\frac{8 x ^{3} + 36 x ^{2} + 54 x + 27}{6} = \frac{8 x ^{3}}{6} + \frac{36 x ^{2}}{6} + \frac{54 x}{6} + \frac{27}{6}

= \frac{8 x ^{3}}{6} + \frac{36 x ^{2}}{6} + \frac{54 x}{6} + \frac{27}{6}

\frac{8 x ^{3}}{6} = \frac{4 x ^{3}}{3}

\frac{36 x ^{2}}{6} = 6 x^{2}

\frac{54 x}{6} = 9 x

\frac{27}{6} = \frac{9}{2}

= \frac{4 x ^{3}}{3} + 6 x^{2} + 9 x + \frac{9}{2}

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