What is (4-sqrt(x+7))^2 ?

The solution to (4-sqrt(x+7))^2 is x-8sqrt(x+7)+23

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simplify (4-sqrt(x+7))^2

simplify

(4 - x + 7)^{2}

x - 8 x + 7 + 23

Solution steps

(4 - x + 7)^{2}

Apply Perfect Square Formula:

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

(4 - x + 7)^{2} = 4^{2} - 2 \cdot 4 x + 7 + (x + 7)^{2}

= 4^{2} - 2 \cdot 4 x + 7 + (x + 7)^{2}

Simplify

4^{2} - 2 \cdot 4 x + 7 + (x + 7)^{2} : x - 8 x + 7 + 23

= x - 8 x + 7 + 23

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