What is (sqrt(3)u-sqrt(3/23)v)^2 ?

The solution to (sqrt(3)u-sqrt(3/23)v)^2 is (69u^2-6sqrt(23)uv+3v^2)/(23)

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simplify (sqrt(3)u-sqrt(3/23)v)^2

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

(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}

Simplify

(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}

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What is (sqrt(3)u-sqrt(3/23)v)^2 ?
The solution to (sqrt(3)u-sqrt(3/23)v)^2 is (69u^2-6sqrt(23)uv+3v^2)/(23)