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

The solution to (4-sqrt(x-2))^2 is x-8sqrt(x-2)+14

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

simplify

(4 - x - 2)^{2}

x - 8 x - 2 + 14

Solution steps

(4 - x - 2)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

4^{2} - 2 \cdot 4 x - 2 + (x - 2)^{2} : x - 8 x - 2 + 14

= x - 8 x - 2 + 14

3 (7 + 2)

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