展开 (x-9/2)^3

解答

展开

(x - \frac{9}{2})^{3}

\frac{8 x ^{3} + 486 x - 108 x ^{2} - 729}{8}

求解步骤

(x - \frac{9}{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}

(x - \frac{9}{2})^{3} = x^{3} - 3 x^{2} \frac{9}{2} + 3 x (\frac{9}{2})^{2} - (\frac{9}{2})^{3}

= x^{3} - 3 x^{2} \frac{9}{2} + 3 x (\frac{9}{2})^{2} - (\frac{9}{2})^{3}

化简

x^{3} - 3 x^{2} \frac{9}{2} + 3 x (\frac{9}{2})^{2} - (\frac{9}{2})^{3} : \frac{8 x ^{3} + 486 x - 108 x ^{2} - 729}{8}

= \frac{8 x ^{3} + 486 x - 108 x ^{2} - 729}{8}

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