展开 (2-x/3)^3

解答

展开

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

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

求解步骤

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

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

化简

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

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

s im pl i f y (x - 2 - 3) (x - 2 + 3)

s im pl i f y (a - x)^{2}

s im pl i f y (x + 1 - x - 1)^{2}

e x p an d \frac{( s + 1 ) ^{3}}{s ^{4}}

e x p an d L im x \Rightarrow \frac{1}{2} (x + 3)