What is (sqrt(2)u+sqrt(2/19)v)^2 ?

The solution to (sqrt(2)u+sqrt(2/19)v)^2 is (38u^2+4sqrt(19)uv+2v^2)/(19)

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simplify (sqrt(2)u+sqrt(2/19)v)^2

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

(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}

Simplify

(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}

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What is (sqrt(2)u+sqrt(2/19)v)^2 ?
The solution to (sqrt(2)u+sqrt(2/19)v)^2 is (38u^2+4sqrt(19)uv+2v^2)/(19)