展開する (2x^3+y^2)^2

解

展開する

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

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

解答ステップ

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

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

簡素化

(2 x^{3})^{2} + 2 \cdot 2 x^{3} y^{2} + (y^{2})^{2} : 4 x^{6} + 4 x^{3} y^{2} + y^{4}

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