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

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

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

simplify

(2 x + x)^{2}

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

Solution steps

(2 x + x)^{2}

Apply Perfect Square Formula:

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

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

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

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

2 \cdot 2 x x = 4 x x

(x)^{2} = x

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

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