What is (2sqrt(x)+1)^2 ?

The solution to (2sqrt(x)+1)^2 is 4x+4sqrt(x)+1

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simplify (2sqrt(x)+1)^2

simplify

(2 x + 1)^{2}

4 x + 4 x + 1

Solution steps

(2 x + 1)^{2}

Apply Perfect Square Formula:

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

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

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

(2 x)^{2} = 4 x

2 \cdot 2 x \cdot 1 = 4 x

1^{2} = 1

= 4 x + 4 x + 1

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