展开 (2-1/3 x)^3

解答

展开

(2 - \frac{1}{3} x)^{3}

\frac{216 - 108 x + 18 x ^{2} - x ^{3}}{27}

求解步骤

(2 - \frac{1}{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}

(2 - \frac{1}{3} x)^{3} = 2^{3} - 3 \cdot 2^{2} \cdot \frac{1}{3} x + 3 \cdot 2 (\frac{1}{3} x)^{2} - (\frac{1}{3} x)^{3}

= 2^{3} - 3 \cdot 2^{2} \cdot \frac{1}{3} x + 3 \cdot 2 (\frac{1}{3} x)^{2} - (\frac{1}{3} x)^{3}

化简

2^{3} - 3 \cdot 2^{2} \cdot \frac{1}{3} x + 3 \cdot 2 (\frac{1}{3} x)^{2} - (\frac{1}{3} x)^{3} : \frac{216 - 108 x + 18 x ^{2} - x ^{3}}{27}

= \frac{216 - 108 x + 18 x ^{2} - x ^{3}}{27}

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

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s im pl i f y (t - \frac{1}{2}) (t - \frac{3}{4})