展開する ((x-1}{2x})(3-\frac{2x)/9)^8

解

展開する

(\frac{x - 1}{2 x}) (3 - \frac{2 x}{9})^{8}

504 x^{2} - 2448 x + \frac{6561 ( x - 1 )}{2 x} - \frac{224 ( x - 1 ) x ^{2}}{3} + \frac{560 ( x - 1 ) x ^{3}}{81} - \frac{896 ( x - 1 ) x ^{4}}{2187} + \frac{896 ( x - 1 ) x ^{5}}{59049} - \frac{512 ( x - 1 ) x ^{6}}{1594323} + \frac{128 ( x - 1 ) x ^{7}}{43046721} + 1944

解答ステップ

(\frac{x - 1}{2 x}) (3 - \frac{2 x}{9})^{8}

規則を適用する:

(a) = a

(\frac{x - 1}{2 x}) = \frac{x - 1}{2 x}

= \frac{x - 1}{2 x} (3 - \frac{2 x}{9})^{8}

拡張

(3 - \frac{2 x}{9})^{8} : 6561 - 3888 x + 1008 x^{2} - \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{81} - \frac{1792 x ^{5}}{2187} + \frac{1792 x ^{6}}{59049} - \frac{1024 x ^{7}}{1594323} + \frac{256 x ^{8}}{43046721}

= \frac{x - 1}{2 x} (6561 - 3888 x + 1008 x^{2} - \frac{448 x ^{3}}{3} + \frac{1120 x ^{4}}{81} - \frac{1792 x ^{5}}{2187} + \frac{1792 x ^{6}}{59049} - \frac{1024 x ^{7}}{1594323} + \frac{256 x ^{8}}{43046721})

括弧を分配する

= \frac{x - 1}{2 x} \cdot 6561 + \frac{x - 1}{2 x} (- 3888 x) + \frac{x - 1}{2 x} \cdot 1008 x^{2} + \frac{x - 1}{2 x} (- \frac{448 x ^{3}}{3}) + \frac{x - 1}{2 x} \cdot \frac{1120 x ^{4}}{81} + \frac{x - 1}{2 x} (- \frac{1792 x ^{5}}{2187}) + \frac{x - 1}{2 x} \cdot \frac{1792 x ^{6}}{59049} + \frac{x - 1}{2 x} (- \frac{1024 x ^{7}}{1594323}) + \frac{x - 1}{2 x} \cdot \frac{256 x ^{8}}{43046721}

簡素化

\frac{x - 1}{2 x} \cdot 6561 + \frac{x - 1}{2 x} (- 3888 x) + \frac{x - 1}{2 x} \cdot 1008 x^{2} + \frac{x - 1}{2 x} (- \frac{448 x ^{3}}{3}) + \frac{x - 1}{2 x} \cdot \frac{1120 x ^{4}}{81} + \frac{x - 1}{2 x} (- \frac{1792 x ^{5}}{2187}) + \frac{x - 1}{2 x} \cdot \frac{1792 x ^{6}}{59049} + \frac{x - 1}{2 x} (- \frac{1024 x ^{7}}{1594323}) + \frac{x - 1}{2 x} \cdot \frac{256 x ^{8}}{43046721} : 504 x^{2} - 2448 x + \frac{6561 ( x - 1 )}{2 x} - \frac{224 ( x - 1 ) x ^{2}}{3} + \frac{560 ( x - 1 ) x ^{3}}{81} - \frac{896 ( x - 1 ) x ^{4}}{2187} + \frac{896 ( x - 1 ) x ^{5}}{59049} - \frac{512 ( x - 1 ) x ^{6}}{1594323} + \frac{128 ( x - 1 ) x ^{7}}{43046721} + 1944

= 504 x^{2} - 2448 x + \frac{6561 ( x - 1 )}{2 x} - \frac{224 ( x - 1 ) x ^{2}}{3} + \frac{560 ( x - 1 ) x ^{3}}{81} - \frac{896 ( x - 1 ) x ^{4}}{2187} + \frac{896 ( x - 1 ) x ^{5}}{59049} - \frac{512 ( x - 1 ) x ^{6}}{1594323} + \frac{128 ( x - 1 ) x ^{7}}{43046721} + 1944