What is (2-4sqrt(x))^2 ?

The solution to (2-4sqrt(x))^2 is 4-16sqrt(x)+16x

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simplify (2-4sqrt(x))^2

simplify

(2 - 4 x)^{2}

4 - 16 x + 16 x

Solution steps

(2 - 4 x)^{2}

Apply Perfect Square Formula:

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

(2 - 4 x)^{2} = 2^{2} - 2 \cdot 2 \cdot 4 x + (4 x)^{2}

= 2^{2} - 2 \cdot 2 \cdot 4 x + (4 x)^{2}

2^{2} = 4

- 2 \cdot 2 \cdot 4 x = - 16 x

(4 x)^{2} = 16 x

= 4 - 16 x + 16 x

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