展开 (4/3-x)^3

解答

展开

(\frac{4}{3} - x)^{3}

\frac{64 - 144 x + 108 x ^{2} - 27 x ^{3}}{27}

求解步骤

(\frac{4}{3} - x)^{3}

使用完全立方公式:

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

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

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

化简

(\frac{4}{3})^{3} - 3 (\frac{4}{3})^{2} x + 3 \cdot \frac{4}{3} x^{2} - x^{3} : \frac{64 - 144 x + 108 x ^{2} - 27 x ^{3}}{27}

= \frac{64 - 144 x + 108 x ^{2} - 27 x ^{3}}{27}

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