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

The solution to (sqrt(x)+2y)^2 is x+4ysqrt(x)+4y^2

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

simplify

(x + 2 y)^{2}

x + 4 y x + 4 y^{2}

Solution steps

(x + 2 y)^{2}

Apply Perfect Square Formula:

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

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

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

(x)^{2} = x

2 x \cdot 2 y = 4 y x

(2 y)^{2} = 4 y^{2}

= x + 4 y x + 4 y^{2}

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