展開する (3+2y+y^2)^5

解

展開する

(3 + 2 y + y^{2})^{5}

y^{10} + 10 y^{9} + 55 y^{8} + 200 y^{7} + 530 y^{6} + 1052 y^{5} + 1590 y^{4} + 1800 y^{3} + 1485 y^{2} + 810 y + 243

解答ステップ

(3 + 2 y + y^{2})^{5}

(3 + 2 y + y^{2})^{5} = (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2})

= (y^{2} + 2 y + 3) (y^{2} + 2 y + 3) (y^{2} + 2 y + 3) (y^{2} + 2 y + 3) (y^{2} + 2 y + 3)

拡張

(3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) (3 + 2 y + y^{2}) : y^{10} + 10 y^{9} + 55 y^{8} + 200 y^{7} + 530 y^{6} + 1052 y^{5} + 1590 y^{4} + 1800 y^{3} + 1485 y^{2} + 810 y + 243

= y^{10} + 10 y^{9} + 55 y^{8} + 200 y^{7} + 530 y^{6} + 1052 y^{5} + 1590 y^{4} + 1800 y^{3} + 1485 y^{2} + 810 y + 243