展開する (2x^3-3y^2)^3

解

展開する

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

8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}

解答ステップ

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

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

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

簡素化

(2 x^{3})^{3} - 3 (2 x^{3})^{2} \cdot 3 y^{2} + 3 \cdot 2 x^{3} (3 y^{2})^{2} - (3 y^{2})^{3} : 8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}

= 8 x^{9} - 36 x^{6} y^{2} + 54 x^{3} y^{4} - 27 y^{6}