簡約 (1/2 x-1/3 y)^3

解

簡約

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

\frac{x ^{3}}{8} - \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} - \frac{y ^{3}}{27}

解答ステップ

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

\frac{1}{2} x = \frac{x}{2}

\frac{1}{3} y = \frac{y}{3}

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

完全立方式を適用する:

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

a = \frac{x}{2}, b = \frac{y}{3}

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

簡素化

(\frac{x}{2})^{3} - 3 (\frac{x}{2})^{2} \frac{y}{3} + 3 \cdot \frac{x}{2} (\frac{y}{3})^{2} - (\frac{y}{3})^{3} : \frac{x ^{3}}{8} - \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} - \frac{y ^{3}}{27}

= \frac{x ^{3}}{8} - \frac{x ^{2} y}{4} + \frac{x y ^{2}}{6} - \frac{y ^{3}}{27}