簡約 (sqrt(2)u+sqrt(2/19)v)^2

解

簡約

(2 u + \frac{2}{19} v)^{2}

\frac{38 u ^{2} + 4 19 uv + 2 v ^{2}}{19}

解答ステップ

(2 u + \frac{2}{19} v)^{2}

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(2 u + \frac{2}{19} v)^{2} = (2 u)^{2} + 22 u \frac{2}{19} v + (\frac{2}{19} v)^{2}

= (2 u)^{2} + 22 u \frac{2}{19} v + (\frac{2}{19} v)^{2}

簡素化

(2 u)^{2} + 22 u \frac{2}{19} v + (\frac{2}{19} v)^{2} : \frac{38 u ^{2} + 38 2 \frac{2}{19} uv + 2 v ^{2}}{19}

= \frac{38 u ^{2} + 38 2 \frac{2}{19} uv + 2 v ^{2}}{19}

382 \frac{2}{19} uv = 419 uv

= \frac{38 u ^{2} + 4 19 uv + 2 v ^{2}}{19}