What is (sqrt(2x)-y)^2 ?

The solution to (sqrt(2x)-y)^2 is 2x-2sqrt(2)ysqrt(x)+y^2

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simplify (sqrt(2x)-y)^2

simplify

(2 x - y)^{2}

2 x - 22 y x + y^{2}

Solution steps

(2 x - y)^{2}

Apply Perfect Square Formula:

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

(2 x - y)^{2} = (2 x)^{2} - 2 2 x y + y^{2}

= (2 x)^{2} - 2 2 x y + y^{2}

(2 x)^{2} = 2 x

- 2 2 x y = - 2 y 2 x

= 2 x - 2 y 2 x + y^{2}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 2 x - 22 y x + y^{2}

x^{2} y^{2} - x^{2} - 1 + y^{2}

x^{2} y^{2} + x^{2} - y^{2} - 1

(2 x - 8)^{3}

\frac{( \frac{2}{x} + \frac{4}{y} )}{( 2 x + y )}

\frac{( x + 1 + 1 - x )}{x}

What is (sqrt(2x)-y)^2 ?
The solution to (sqrt(2x)-y)^2 is 2x-2sqrt(2)ysqrt(x)+y^2