展開する (2x^2+5y^4)^3

解

展開する

(2 x^{2} + 5 y^{4})^{3}

8 x^{6} + 60 x^{4} y^{4} + 150 x^{2} y^{8} + 125 y^{12}

解答ステップ

(2 x^{2} + 5 y^{4})^{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^{2} + 5 y^{4})^{3} = (2 x^{2})^{3} + 3 (2 x^{2})^{2} \cdot 5 y^{4} + 3 \cdot 2 x^{2} (5 y^{4})^{2} + (5 y^{4})^{3}

= (2 x^{2})^{3} + 3 (2 x^{2})^{2} \cdot 5 y^{4} + 3 \cdot 2 x^{2} (5 y^{4})^{2} + (5 y^{4})^{3}

簡素化

(2 x^{2})^{3} + 3 (2 x^{2})^{2} \cdot 5 y^{4} + 3 \cdot 2 x^{2} (5 y^{4})^{2} + (5 y^{4})^{3} : 8 x^{6} + 60 x^{4} y^{4} + 150 x^{2} y^{8} + 125 y^{12}

= 8 x^{6} + 60 x^{4} y^{4} + 150 x^{2} y^{8} + 125 y^{12}