簡約 (sqrt(3)u-sqrt(3/23)v)^2

解

簡約

(3 u - \frac{3}{23} v)^{2}

\frac{69 u ^{2} - 6 23 uv + 3 v ^{2}}{23}

解答ステップ

(3 u - \frac{3}{23} v)^{2}

完全平方式を適用する:

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

(3 u - \frac{3}{23} v)^{2} = (3 u)^{2} - 23 u \frac{3}{23} v + (\frac{3}{23} v)^{2}

= (3 u)^{2} - 23 u \frac{3}{23} v + (\frac{3}{23} v)^{2}

簡素化

(3 u)^{2} - 23 u \frac{3}{23} v + (\frac{3}{23} v)^{2} : \frac{69 u ^{2} - 46 3 \frac{3}{23} uv + 3 v ^{2}}{23}

= \frac{69 u ^{2} - 46 3 \frac{3}{23} uv + 3 v ^{2}}{23}

463 \frac{3}{23} uv = 623 uv

= \frac{69 u ^{2} - 6 23 uv + 3 v ^{2}}{23}