What is expand (x^{1/2}-2y^{1/2})^2 ?

The solution to expand (x^{1/2}-2y^{1/2})^2 is x-4x^{1/2}y^{1/2}+4y

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expand (x^{1/2}-2y^{1/2})^2

expand

(x^{\frac{1}{2}} - 2 y^{\frac{1}{2}})^{2}

x - 4 x^{\frac{1}{2}} y^{\frac{1}{2}} + 4 y

Solution steps

(x^{\frac{1}{2}} - 2 y^{\frac{1}{2}})^{2}

Apply Perfect Square Formula:

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

(x^{\frac{1}{2}} - 2 y^{\frac{1}{2}})^{2} = (x^{\frac{1}{2}})^{2} - 2 x^{\frac{1}{2}} \cdot 2 y^{\frac{1}{2}} + (2 y^{\frac{1}{2}})^{2}

= (x^{\frac{1}{2}})^{2} - 2 x^{\frac{1}{2}} \cdot 2 y^{\frac{1}{2}} + (2 y^{\frac{1}{2}})^{2}

(x^{\frac{1}{2}})^{2} = x

2 x^{\frac{1}{2}} \cdot 2 y^{\frac{1}{2}} = 4 x^{\frac{1}{2}} y^{\frac{1}{2}}

(2 y^{\frac{1}{2}})^{2} = 4 y

= x - 4 x^{\frac{1}{2}} y^{\frac{1}{2}} + 4 y

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What is expand (x^{1/2}-2y^{1/2})^2 ?
The solution to expand (x^{1/2}-2y^{1/2})^2 is x-4x^{1/2}y^{1/2}+4y