展開する (3+4x^3)(2x^2-1/(2x))^{12}

解

展開する

(3 + 4 x^{3}) (2 x^{2} - \frac{1}{2 x})^{12}

\frac{3 ( 4 x ^{3} - 1 ) ^{12}}{4096 x ^{12}} + \frac{( 4 x ^{3} - 1 ) ^{12}}{1024 x ^{9}}

解答ステップ

(3 + 4 x^{3}) (2 x^{2} - \frac{1}{2 x})^{12}

= (2 x^{2} - \frac{1}{2 x})^{12} (3 + 4 x^{3})

分配法則を適用する:

a (b + c) = ab + a c

(2 x^{2} - \frac{1}{2 x})^{12} (3 + 4 x^{3}) = (2 x^{2} - \frac{1}{2 x})^{12} \cdot 3 + (2 x^{2} - \frac{1}{2 x})^{12} \cdot 4 x^{3}

= (2 x^{2} - \frac{1}{2 x})^{12} \cdot 3 + (2 x^{2} - \frac{1}{2 x})^{12} \cdot 4 x^{3}

簡素化

(2 x^{2} - \frac{1}{2 x})^{12} \cdot 3 + (2 x^{2} - \frac{1}{2 x})^{12} \cdot 4 x^{3} : \frac{3 ( 4 x ^{3} - 1 ) ^{12}}{4096 x ^{12}} + \frac{( 4 x ^{3} - 1 ) ^{12}}{1024 x ^{9}}

= \frac{3 ( 4 x ^{3} - 1 ) ^{12}}{4096 x ^{12}} + \frac{( 4 x ^{3} - 1 ) ^{12}}{1024 x ^{9}}