展开 (3x^2+7y)^3

解答

展开

(3 x^{2} + 7 y)^{3}

27 x^{6} + 189 x^{4} y + 441 x^{2} y^{2} + 343 y^{3}

求解步骤

(3 x^{2} + 7 y)^{3}

使用完全立方公式:

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

(3 x^{2} + 7 y)^{3} = (3 x^{2})^{3} + 3 (3 x^{2})^{2} \cdot 7 y + 3 \cdot 3 x^{2} (7 y)^{2} + (7 y)^{3}

= (3 x^{2})^{3} + 3 (3 x^{2})^{2} \cdot 7 y + 3 \cdot 3 x^{2} (7 y)^{2} + (7 y)^{3}

化简

(3 x^{2})^{3} + 3 (3 x^{2})^{2} \cdot 7 y + 3 \cdot 3 x^{2} (7 y)^{2} + (7 y)^{3} : 27 x^{6} + 189 x^{4} y + 441 x^{2} y^{2} + 343 y^{3}

= 27 x^{6} + 189 x^{4} y + 441 x^{2} y^{2} + 343 y^{3}

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