展開する 4(x^{1/3}+1)^7

解

展開する

4 (x^{\frac{1}{3}} + 1)^{7}

4 x^{\frac{7}{3}} + 28 x^{2} + 84 x^{\frac{5}{3}} + 140 x^{\frac{4}{3}} + 140 x + 84 x^{\frac{2}{3}} + 28 x^{\frac{1}{3}} + 4

解答ステップ

4 (x^{\frac{1}{3}} + 1)^{7}

拡張

(x^{\frac{1}{3}} + 1)^{7} : x^{\frac{7}{3}} + 7 x^{2} + 21 x^{\frac{5}{3}} + 35 x^{\frac{4}{3}} + 35 x + 21 x^{\frac{2}{3}} + 7 x^{\frac{1}{3}} + 1

= 4 (x^{\frac{7}{3}} + 7 x^{2} + 21 x^{\frac{5}{3}} + 35 x^{\frac{4}{3}} + 35 x + 21 x^{\frac{2}{3}} + 7 x^{\frac{1}{3}} + 1)

括弧を分配する

= 4 x^{\frac{7}{3}} + 4 \cdot 7 x^{2} + 4 \cdot 21 x^{\frac{5}{3}} + 4 \cdot 35 x^{\frac{4}{3}} + 4 \cdot 35 x + 4 \cdot 21 x^{\frac{2}{3}} + 4 \cdot 7 x^{\frac{1}{3}} + 4 \cdot 1

4 \cdot 7 x^{2} = 28 x^{2}

4 \cdot 21 x^{\frac{5}{3}} = 84 x^{\frac{5}{3}}

4 \cdot 35 x^{\frac{4}{3}} = 140 x^{\frac{4}{3}}

4 \cdot 35 x = 140 x

4 \cdot 21 x^{\frac{2}{3}} = 84 x^{\frac{2}{3}}

4 \cdot 7 x^{\frac{1}{3}} = 28 x^{\frac{1}{3}}

4 \cdot 1 = 4

= 4 x^{\frac{7}{3}} + 28 x^{2} + 84 x^{\frac{5}{3}} + 140 x^{\frac{4}{3}} + 140 x + 84 x^{\frac{2}{3}} + 28 x^{\frac{1}{3}} + 4