展開する (x^3+3)^6(3x^2)dx

解

展開する

(x^{3} + 3)^{6} (3 x^{2}) d x

3 x^{20} d x + 54 x^{17} d x + 405 x^{14} d x + 1620 x^{11} d x + 3645 x^{8} d x + 4374 x^{5} d x + 2187 x^{2} d x

解答ステップ

(x^{3} + 3)^{6} (3 x^{2}) d x

括弧を削除する:

(a) = a

= (x^{3} + 3)^{6} \cdot 3 x^{2} d x

(x^{3} + 3)^{6} = x^{18} + 18 x^{15} + 135 x^{12} + 540 x^{9} + 1215 x^{6} + 1458 x^{3} + 729

= 3 x^{2} (x^{18} + 18 x^{15} + 135 x^{12} + 540 x^{9} + 1215 x^{6} + 1458 x^{3} + 729) d x

= 3 x^{2} (x^{18} + 18 x^{15} + 135 x^{12} + 540 x^{9} + 1215 x^{6} + 1458 x^{3} + 729) d x

括弧を分配する

= 3 x^{2} d x x^{18} + 3 x^{2} d x \cdot 18 x^{15} + 3 x^{2} d x \cdot 135 x^{12} + 3 x^{2} d x \cdot 540 x^{9} + 3 x^{2} d x \cdot 1215 x^{6} + 3 x^{2} d x \cdot 1458 x^{3} + 3 x^{2} d x \cdot 729

= 3 x^{18} x^{2} d x + 3 \cdot 18 x^{15} x^{2} d x + 3 \cdot 135 x^{12} x^{2} d x + 3 \cdot 540 x^{9} x^{2} d x + 3 \cdot 1215 x^{6} x^{2} d x + 3 \cdot 1458 x^{3} x^{2} d x + 3 \cdot 729 x^{2} d x

簡素化

3 x^{18} x^{2} d x + 3 \cdot 18 x^{15} x^{2} d x + 3 \cdot 135 x^{12} x^{2} d x + 3 \cdot 540 x^{9} x^{2} d x + 3 \cdot 1215 x^{6} x^{2} d x + 3 \cdot 1458 x^{3} x^{2} d x + 3 \cdot 729 x^{2} d x : 3 x^{20} d x + 54 x^{17} d x + 405 x^{14} d x + 1620 x^{11} d x + 3645 x^{8} d x + 4374 x^{5} d x + 2187 x^{2} d x

= 3 x^{20} d x + 54 x^{17} d x + 405 x^{14} d x + 1620 x^{11} d x + 3645 x^{8} d x + 4374 x^{5} d x + 2187 x^{2} d x