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

The solution to (4-sqrt(4+x))^2 is x-8sqrt(4+x)+20

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

simplify

(4 - 4 + x)^{2}

x - 8 4 + x + 20

Solution steps

(4 - 4 + x)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

4^{2} - 2 \cdot 4 4 + x + (4 + x)^{2} : x - 8 4 + x + 20

= x - 8 4 + x + 20

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