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

The solution to (sqrt(x+2)-4)^2 is x-8sqrt(x+2)+18

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

simplify

(x + 2 - 4)^{2}

x - 8 x + 2 + 18

Solution steps

(x + 2 - 4)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

(x + 2)^{2} - 2 x + 2 \cdot 4 + 4^{2} : x - 8 x + 2 + 18

= x - 8 x + 2 + 18

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