展開する (5x^3*y^2-x)^3

解

展開する

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

125 x^{9} y^{6} - 75 x^{7} y^{4} + 15 x^{5} y^{2} - x^{3}

解答ステップ

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

(5 x^{3} y^{2} - x)^{3} = (5 x^{3} y^{2})^{3} - 3 (5 x^{3} y^{2})^{2} x + 3 \cdot 5 x^{3} y^{2} x^{2} - x^{3}

= (5 x^{3} y^{2})^{3} - 3 (5 x^{3} y^{2})^{2} x + 3 \cdot 5 x^{3} y^{2} x^{2} - x^{3}

簡素化

(5 x^{3} y^{2})^{3} - 3 (5 x^{3} y^{2})^{2} x + 3 \cdot 5 x^{3} y^{2} x^{2} - x^{3} : 125 x^{9} y^{6} - 75 x^{7} y^{4} + 15 x^{5} y^{2} - x^{3}

= 125 x^{9} y^{6} - 75 x^{7} y^{4} + 15 x^{5} y^{2} - x^{3}