展開する (1+2/3 x)^6(3+6x)^2

解

展開する

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

9 + 72 x + 240 x^{2} + \frac{1312 x ^{3}}{3} + 480 x^{4} + \frac{2944 x ^{5}}{9} + \frac{11008 x ^{6}}{81} + \frac{2560 x ^{7}}{81} + \frac{256 x ^{8}}{81}

解答ステップ

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

拡張

(3 + 6 x)^{2} : 9 + 36 x + 36 x^{2}

= (1 + \frac{2}{3} x)^{6} (9 + 36 x + 36 x^{2})

分配法則を適用する:

m (a + b + c) = ma + mb + m c

(1 + \frac{2}{3} x)^{6} (9 + 36 x + 36 x^{2}) = (1 + \frac{2}{3} x)^{6} \cdot 9 + (1 + \frac{2}{3} x)^{6} \cdot 36 x + (1 + \frac{2}{3} x)^{6} \cdot 36 x^{2}

= (1 + \frac{2}{3} x)^{6} \cdot 9 + (1 + \frac{2}{3} x)^{6} \cdot 36 x + (1 + \frac{2}{3} x)^{6} \cdot 36 x^{2}

= 9 (1 + \frac{2}{3} x)^{6} + 36 x (1 + \frac{2}{3} x)^{6} + 36 x^{2} (1 + \frac{2}{3} x)^{6}

拡張

9 (1 + \frac{2}{3} x)^{6} : 9 + 36 x + 60 x^{2} + \frac{160 x ^{3}}{3} + \frac{80 x ^{4}}{3} + \frac{64 x ^{5}}{9} + \frac{64 x ^{6}}{81}

= 9 + 36 x + 60 x^{2} + \frac{160 x ^{3}}{3} + \frac{80 x ^{4}}{3} + \frac{64 x ^{5}}{9} + \frac{64 x ^{6}}{81} + 36 x (1 + \frac{2}{3} x)^{6} + 36 x^{2} (1 + \frac{2}{3} x)^{6}

拡張

36 x (1 + \frac{2}{3} x)^{6} : 36 x + 144 x^{2} + 240 x^{3} + \frac{640 x ^{4}}{3} + \frac{320 x ^{5}}{3} + \frac{256 x ^{6}}{9} + \frac{256 x ^{7}}{81}

= 9 + 36 x + 60 x^{2} + \frac{160 x ^{3}}{3} + \frac{80 x ^{4}}{3} + \frac{64 x ^{5}}{9} + \frac{64 x ^{6}}{81} + 36 x + 144 x^{2} + 240 x^{3} + \frac{640 x ^{4}}{3} + \frac{320 x ^{5}}{3} + \frac{256 x ^{6}}{9} + \frac{256 x ^{7}}{81} + 36 x^{2} (1 + \frac{2}{3} x)^{6}

拡張

36 x^{2} (1 + \frac{2}{3} x)^{6} : 36 x^{2} + 144 x^{3} + 240 x^{4} + \frac{640 x ^{5}}{3} + \frac{320 x ^{6}}{3} + \frac{256 x ^{7}}{9} + \frac{256 x ^{8}}{81}

= 9 + 36 x + 60 x^{2} + \frac{160 x ^{3}}{3} + \frac{80 x ^{4}}{3} + \frac{64 x ^{5}}{9} + \frac{64 x ^{6}}{81} + 36 x + 144 x^{2} + 240 x^{3} + \frac{640 x ^{4}}{3} + \frac{320 x ^{5}}{3} + \frac{256 x ^{6}}{9} + \frac{256 x ^{7}}{81} + 36 x^{2} + 144 x^{3} + 240 x^{4} + \frac{640 x ^{5}}{3} + \frac{320 x ^{6}}{3} + \frac{256 x ^{7}}{9} + \frac{256 x ^{8}}{81}

簡素化

9 + 36 x + 60 x^{2} + \frac{160 x ^{3}}{3} + \frac{80 x ^{4}}{3} + \frac{64 x ^{5}}{9} + \frac{64 x ^{6}}{81} + 36 x + 144 x^{2} + 240 x^{3} + \frac{640 x ^{4}}{3} + \frac{320 x ^{5}}{3} + \frac{256 x ^{6}}{9} + \frac{256 x ^{7}}{81} + 36 x^{2} + 144 x^{3} + 240 x^{4} + \frac{640 x ^{5}}{3} + \frac{320 x ^{6}}{3} + \frac{256 x ^{7}}{9} + \frac{256 x ^{8}}{81} : 9 + 72 x + 240 x^{2} + \frac{1312 x ^{3}}{3} + 480 x^{4} + \frac{2944 x ^{5}}{9} + \frac{11008 x ^{6}}{81} + \frac{2560 x ^{7}}{81} + \frac{256 x ^{8}}{81}

= 9 + 72 x + 240 x^{2} + \frac{1312 x ^{3}}{3} + 480 x^{4} + \frac{2944 x ^{5}}{9} + \frac{11008 x ^{6}}{81} + \frac{2560 x ^{7}}{81} + \frac{256 x ^{8}}{81}