展開する (4a^4+7b^2)^3

解

展開する

(4 a^{4} + 7 b^{2})^{3}

64 a^{12} + 336 a^{8} b^{2} + 588 a^{4} b^{4} + 343 b^{6}

解答ステップ

(4 a^{4} + 7 b^{2})^{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}

(4 a^{4} + 7 b^{2})^{3} = (4 a^{4})^{3} + 3 (4 a^{4})^{2} \cdot 7 b^{2} + 3 \cdot 4 a^{4} (7 b^{2})^{2} + (7 b^{2})^{3}

= (4 a^{4})^{3} + 3 (4 a^{4})^{2} \cdot 7 b^{2} + 3 \cdot 4 a^{4} (7 b^{2})^{2} + (7 b^{2})^{3}

簡素化

(4 a^{4})^{3} + 3 (4 a^{4})^{2} \cdot 7 b^{2} + 3 \cdot 4 a^{4} (7 b^{2})^{2} + (7 b^{2})^{3} : 64 a^{12} + 336 a^{8} b^{2} + 588 a^{4} b^{4} + 343 b^{6}

= 64 a^{12} + 336 a^{8} b^{2} + 588 a^{4} b^{4} + 343 b^{6}