展开 ((4x+1)^3)/(12)

解答

展开

\frac{( 4 x + 1 ) ^{3}}{12}

\frac{16 x ^{3}}{3} + 4 x^{2} + x + \frac{1}{12}

求解步骤

\frac{( 4 x + 1 ) ^{3}}{12}

(4 x + 1)^{3} = 64 x^{3} + 48 x^{2} + 12 x + 1

= \frac{64 x ^{3} + 48 x ^{2} + 12 x + 1}{12}

使用分式法则:

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

\frac{64 x ^{3} + 48 x ^{2} + 12 x + 1}{12} = \frac{64 x ^{3}}{12} + \frac{48 x ^{2}}{12} + \frac{12 x}{12} + \frac{1}{12}

= \frac{64 x ^{3}}{12} + \frac{48 x ^{2}}{12} + \frac{12 x}{12} + \frac{1}{12}

消掉

\frac{64 x ^{3}}{12} : \frac{16 x ^{3}}{3}

= \frac{16 x ^{3}}{3} + \frac{48 x ^{2}}{12} + \frac{12 x}{12} + \frac{1}{12}

数字相除:

\frac{48}{12} = 4

= \frac{16 x ^{3}}{3} + 4 x^{2} + \frac{12 x}{12} + \frac{1}{12}

数字相除:

\frac{12}{12} = 1

= \frac{16 x ^{3}}{3} + 4 x^{2} + x + \frac{1}{12}

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