展開する (5x^2+7y^3)^3

解

展開する

(5 x^{2} + 7 y^{3})^{3}

125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}

解答ステップ

(5 x^{2} + 7 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}

(5 x^{2} + 7 y^{3})^{3} = (5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3}

= (5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3}

簡素化

(5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3} : 125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}

= 125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}