簡約 (2x^2-y)^3-(2x-y^2)^3+2xy(3x+y)

解

簡約

(2 x^{2} - y)^{3} - (2 x - y^{2})^{3} + 2 x y (3 x + y)

8 x^{6} + y^{6} - 12 x^{4} y - y^{3} - 8 x^{3} + 18 x^{2} y^{2} - 6 x y^{4} + 6 x^{2} y + 2 x y^{2}

解答ステップ

(2 x^{2} - y)^{3} - (2 x - y^{2})^{3} + 2 x y (3 x + y)

拡張

(2 x^{2} - y)^{3} : 8 x^{6} - 12 x^{4} y + 6 x^{2} y^{2} - y^{3}

= 8 x^{6} - 12 x^{4} y + 6 x^{2} y^{2} - y^{3} - (2 x - y^{2})^{3} + 2 x y (3 x + y)

拡張

- (2 x - y^{2})^{3} : - 8 x^{3} + 12 x^{2} y^{2} - 6 x y^{4} + y^{6}

= 8 x^{6} - 12 x^{4} y + 6 x^{2} y^{2} - y^{3} - 8 x^{3} + 12 x^{2} y^{2} - 6 x y^{4} + y^{6} + 2 x y (3 x + y)

拡張

2 x y (3 x + y) : 6 x^{2} y + 2 x y^{2}

= 8 x^{6} - 12 x^{4} y + 6 x^{2} y^{2} - y^{3} - 8 x^{3} + 12 x^{2} y^{2} - 6 x y^{4} + y^{6} + 6 x^{2} y + 2 x y^{2}

条件のようなグループ

= 8 x^{6} + y^{6} - 12 x^{4} y - y^{3} - 8 x^{3} + 6 x^{2} y^{2} + 12 x^{2} y^{2} - 6 x y^{4} + 6 x^{2} y + 2 x y^{2}

類似した元を足す:

6 x^{2} y^{2} + 12 x^{2} y^{2} = 18 x^{2} y^{2}

= 8 x^{6} + y^{6} - 12 x^{4} y - y^{3} - 8 x^{3} + 18 x^{2} y^{2} - 6 x y^{4} + 6 x^{2} y + 2 x y^{2}