展開する (Ax+B)(x^4+2x^3+5x^2+4x+4)(x^6+3x^4+3x^2+1)

解

展開する

(A x + B) (x^{4} + 2 x^{3} + 5 x^{2} + 4 x + 4) (x^{6} + 3 x^{4} + 3 x^{2} + 1)

A x^{11} + 2 A x^{10} + B x^{10} + 8 A x^{9} + 2 B x^{9} + 10 A x^{8} + 8 B x^{8} + 22 A x^{7} + 10 B x^{7} + 18 A x^{6} + 22 B x^{6} + 28 A x^{5} + 18 B x^{5} + 14 A x^{4} + 28 B x^{4} + 17 A x^{3} + 14 B x^{3} + 4 A x^{2} + 17 B x^{2} + 4 A x + 4 B x + 4 B

解答ステップ

(A x + B) (x^{4} + 2 x^{3} + 5 x^{2} + 4 x + 4) (x^{6} + 3 x^{4} + 3 x^{2} + 1)

拡張

(A x + B) (x^{4} + 2 x^{3} + 5 x^{2} + 4 x + 4) : A x^{5} + 2 A x^{4} + 5 A x^{3} + 4 A x^{2} + 4 A x + B x^{4} + 2 B x^{3} + 5 B x^{2} + 4 B x + 4 B

= (A x^{5} + 2 A x^{4} + 5 A x^{3} + 4 A x^{2} + 4 A x + B x^{4} + 2 B x^{3} + 5 B x^{2} + 4 B x + 4 B) (x^{6} + 3 x^{4} + 3 x^{2} + 1)

拡張

(A x^{5} + 2 A x^{4} + 5 A x^{3} + 4 A x^{2} + 4 A x + B x^{4} + 2 B x^{3} + 5 B x^{2} + 4 B x + 4 B) (x^{6} + 3 x^{4} + 3 x^{2} + 1) : A x^{11} + 2 A x^{10} + B x^{10} + 8 A x^{9} + 2 B x^{9} + 10 A x^{8} + 8 B x^{8} + 22 A x^{7} + 10 B x^{7} + 18 A x^{6} + 22 B x^{6} + 28 A x^{5} + 18 B x^{5} + 14 A x^{4} + 28 B x^{4} + 17 A x^{3} + 14 B x^{3} + 4 A x^{2} + 17 B x^{2} + 4 A x + 4 B x + 4 B

= A x^{11} + 2 A x^{10} + B x^{10} + 8 A x^{9} + 2 B x^{9} + 10 A x^{8} + 8 B x^{8} + 22 A x^{7} + 10 B x^{7} + 18 A x^{6} + 22 B x^{6} + 28 A x^{5} + 18 B x^{5} + 14 A x^{4} + 28 B x^{4} + 17 A x^{3} + 14 B x^{3} + 4 A x^{2} + 17 B x^{2} + 4 A x + 4 B x + 4 B