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

The solution to (sqrt(2)u+sqrt((2v)/3))^2 is (6u^2+6sqrt(2)usqrt((2v)/3)+2v)/(3)

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simplify (sqrt(2)u+sqrt((2v)/3))^2

simplify

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

\frac{6 u ^{2} + 6 2 u \frac{2 v}{3} + 2 v}{3}

Solution steps

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

Apply Perfect Square Formula:

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

(2 u + \frac{2 v}{3})^{2} = (2 u)^{2} + 22 u \frac{2 v}{3} + (\frac{2 v}{3})^{2}

= (2 u)^{2} + 22 u \frac{2 v}{3} + (\frac{2 v}{3})^{2}

Simplify

(2 u)^{2} + 22 u \frac{2 v}{3} + (\frac{2 v}{3})^{2} : \frac{6 u ^{2} + 6 2 u \frac{2 v}{3} + 2 v}{3}

= \frac{6 u ^{2} + 6 2 u \frac{2 v}{3} + 2 v}{3}

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w (1 + \frac{u ^{2}}{w ^{2}})

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f^{'} (1) (x^{2} - 2 x + \frac{1}{x ^{2}})

What is (sqrt(2)u+sqrt((2v)/3))^2 ?
The solution to (sqrt(2)u+sqrt((2v)/3))^2 is (6u^2+6sqrt(2)usqrt((2v)/3)+2v)/(3)