展開する ((9a+1)^3)/(27)

解

展開する

\frac{( 9 a + 1 ) ^{3}}{27}

27 a^{3} + 9 a^{2} + a + \frac{1}{27}

解答ステップ

\frac{( 9 a + 1 ) ^{3}}{27}

(9 a + 1)^{3} = 729 a^{3} + 243 a^{2} + 27 a + 1

= \frac{729 a ^{3} + 243 a ^{2} + 27 a + 1}{27}

分数の規則を適用する:

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

\frac{729 a ^{3} + 243 a ^{2} + 27 a + 1}{27} = \frac{729 a ^{3}}{27} + \frac{243 a ^{2}}{27} + \frac{27 a}{27} + \frac{1}{27}

= \frac{729 a ^{3}}{27} + \frac{243 a ^{2}}{27} + \frac{27 a}{27} + \frac{1}{27}

数を割る:

\frac{729}{27} = 27

= 27 a^{3} + \frac{243 a ^{2}}{27} + \frac{27 a}{27} + \frac{1}{27}

数を割る:

\frac{243}{27} = 9

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

数を割る:

\frac{27}{27} = 1

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