What is (sqrt(mE)+sqrt(m(E-U)))^2 ?

The solution to (sqrt(mE)+sqrt(m(E-U)))^2 is 2mE-mU+2msqrt(E)sqrt(E-U)

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simplify (sqrt(mE)+sqrt(m(E-U)))^2

simplify

(m E + m (E - U))^{2}

2 m E - m U + 2 m E E - U

Solution steps

(m E + m (E - U))^{2}

Apply Perfect Square Formula:

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

(m E + m (E - U))^{2} = (m E)^{2} + 2 m E m (E - U) + (m (E - U))^{2}

= (m E)^{2} + 2 m E m (E - U) + (m (E - U))^{2}

Simplify

(m E)^{2} + 2 m E m (E - U) + (m (E - U))^{2} : 2 m E - m U + 2 m E E - U

= 2 m E - m U + 2 m E E - U

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What is (sqrt(mE)+sqrt(m(E-U)))^2 ?
The solution to (sqrt(mE)+sqrt(m(E-U)))^2 is 2mE-mU+2msqrt(E)sqrt(E-U)