展開する (1+x+3x^2)^6

解

展開する

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

729 x^{12} + 1458 x^{11} + 2673 x^{10} + 2970 x^{9} + 2970 x^{8} + 2178 x^{7} + 1441 x^{6} + 726 x^{5} + 330 x^{4} + 110 x^{3} + 33 x^{2} + 6 x + 1

解答ステップ

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

(1 + x + 3 x^{2})^{6} = (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2})

= (3 x^{2} + x + 1) (3 x^{2} + x + 1) (3 x^{2} + x + 1) (3 x^{2} + x + 1) (3 x^{2} + x + 1) (3 x^{2} + x + 1)

拡張

(1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) (1 + x + 3 x^{2}) : 729 x^{12} + 1458 x^{11} + 2673 x^{10} + 2970 x^{9} + 2970 x^{8} + 2178 x^{7} + 1441 x^{6} + 726 x^{5} + 330 x^{4} + 110 x^{3} + 33 x^{2} + 6 x + 1

= 729 x^{12} + 1458 x^{11} + 2673 x^{10} + 2970 x^{9} + 2970 x^{8} + 2178 x^{7} + 1441 x^{6} + 726 x^{5} + 330 x^{4} + 110 x^{3} + 33 x^{2} + 6 x + 1