展開する (3+2x+4x^2)^5

解

展開する

(3 + 2 x + 4 x^{2})^{5}

1024 x^{10} + 2560 x^{9} + 6400 x^{8} + 8960 x^{7} + 11840 x^{6} + 10592 x^{5} + 8880 x^{4} + 5040 x^{3} + 2700 x^{2} + 810 x + 243

解答ステップ

(3 + 2 x + 4 x^{2})^{5}

(3 + 2 x + 4 x^{2})^{5} = (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2})

= (4 x^{2} + 2 x + 3) (4 x^{2} + 2 x + 3) (4 x^{2} + 2 x + 3) (4 x^{2} + 2 x + 3) (4 x^{2} + 2 x + 3)

拡張

(3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) (3 + 2 x + 4 x^{2}) : 1024 x^{10} + 2560 x^{9} + 6400 x^{8} + 8960 x^{7} + 11840 x^{6} + 10592 x^{5} + 8880 x^{4} + 5040 x^{3} + 2700 x^{2} + 810 x + 243

= 1024 x^{10} + 2560 x^{9} + 6400 x^{8} + 8960 x^{7} + 11840 x^{6} + 10592 x^{5} + 8880 x^{4} + 5040 x^{3} + 2700 x^{2} + 810 x + 243