展开 (4x^3-8y^2)^3

解答

展开

(4 x^{3} - 8 y^{2})^{3}

64 x^{9} - 384 x^{6} y^{2} + 768 x^{3} y^{4} - 512 y^{6}

求解步骤

(4 x^{3} - 8 y^{2})^{3}

使用完全立方公式:

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

(4 x^{3} - 8 y^{2})^{3} = (4 x^{3})^{3} - 3 (4 x^{3})^{2} \cdot 8 y^{2} + 3 \cdot 4 x^{3} (8 y^{2})^{2} - (8 y^{2})^{3}

= (4 x^{3})^{3} - 3 (4 x^{3})^{2} \cdot 8 y^{2} + 3 \cdot 4 x^{3} (8 y^{2})^{2} - (8 y^{2})^{3}

化简

(4 x^{3})^{3} - 3 (4 x^{3})^{2} \cdot 8 y^{2} + 3 \cdot 4 x^{3} (8 y^{2})^{2} - (8 y^{2})^{3} : 64 x^{9} - 384 x^{6} y^{2} + 768 x^{3} y^{4} - 512 y^{6}

= 64 x^{9} - 384 x^{6} y^{2} + 768 x^{3} y^{4} - 512 y^{6}

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s im pl i f y \frac{( n - 1 ) ! ( n - 2 ) !}{( n ! ) ^{2}}

e x p an d (3 x - 6 y - 1)^{3}

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