簡約 (\sqrt[3]{2}a-sqrt(2)b)^2

解

簡約

(32 a - 2 b)^{2}

3 2^{2} a^{2} - 6 2^{5} \cdot 2 ab + 2 b^{2}

解答ステップ

(32 a - 2 b)^{2}

完全平方式を適用する:

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

(32 a - 2 b)^{2} = (32 a)^{2} - 232 a 2 b + (2 b)^{2}

= (32 a)^{2} - 232 a 2 b + (2 b)^{2}

簡素化

(32 a)^{2} - 232 a 2 b + (2 b)^{2} : 2^{\frac{2}{3}} a^{2} - 2 \cdot 2^{\frac{5}{6}} ab + 2 b^{2}

= 2^{\frac{2}{3}} a^{2} - 2 \cdot 2^{\frac{5}{6}} ab + 2 b^{2}

= 2^{\frac{2}{3}} a^{2} - 2^{\frac{5}{6}} \cdot 2 ab + 2 b^{2}

2^{\frac{2}{3}} = 3 2^{2}

= 3 2^{2} a^{2} - 6 2^{5} \cdot 2 ab + 2 b^{2}

2^{\frac{5}{6}} = 6 2^{5}

= 3 2^{2} a^{2} - 6 2^{5} \cdot 2 ab + 2 b^{2}