簡約 (2/3x^2-1/2y)^3

解

簡約

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

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

解答ステップ

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

\frac{2}{3} x^{2} = \frac{2 x ^{2}}{3}

\frac{1}{2} y = \frac{y}{2}

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

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

簡素化

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

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