展开 (17f^2+4e^5)^3

解答

展开

(17 f^{2} + 4 e^{5})^{3}

4913 f^{6} + 3468 e^{5} f^{4} + 816 e^{10} f^{2} + 64 e^{15}

求解步骤

(17 f^{2} + 4 e^{5})^{3}

使用完全立方公式:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = 17 f^{2}, b = 4 e^{5}

= (17 f^{2})^{3} + 3 (17 f^{2})^{2} \cdot 4 e^{5} + 3 \cdot 17 f^{2} (4 e^{5})^{2} + (4 e^{5})^{3}

化简

(17 f^{2})^{3} + 3 (17 f^{2})^{2} \cdot 4 e^{5} + 3 \cdot 17 f^{2} (4 e^{5})^{2} + (4 e^{5})^{3} : 4913 f^{6} + 3468 e^{5} f^{4} + 816 e^{10} f^{2} + 64 e^{15}

= 4913 f^{6} + 3468 e^{5} f^{4} + 816 e^{10} f^{2} + 64 e^{15}

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