展開する (x^2-y^3)^3

解

展開する

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

x^{6} - 3 x^{4} y^{3} + 3 x^{2} y^{6} - y^{9}

解答ステップ

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

完全立方式を適用する:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

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

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

簡素化

(x^{2})^{3} - 3 (x^{2})^{2} y^{3} + 3 x^{2} (y^{3})^{2} - (y^{3})^{3} : x^{6} - 3 x^{4} y^{3} + 3 x^{2} y^{6} - y^{9}

= x^{6} - 3 x^{4} y^{3} + 3 x^{2} y^{6} - y^{9}