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

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

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

simplify

(2 x - x)^{2}

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

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 \cdot 2 x x = - 4 x x

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

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