展開する (4ab^2+5xy^3)^2

解

展開する

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

16 a^{2} b^{4} + 40 a x b^{2} y^{3} + 25 x^{2} y^{6}

解答ステップ

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

完全平方式を適用する:

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

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

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

簡素化

(4 a b^{2})^{2} + 2 \cdot 4 a b^{2} \cdot 5 x y^{3} + (5 x y^{3})^{2} : 16 a^{2} b^{4} + 40 a x b^{2} y^{3} + 25 x^{2} y^{6}

= 16 a^{2} b^{4} + 40 a x b^{2} y^{3} + 25 x^{2} y^{6}