What is (sqrt(x-4)+1)^2 ?

The solution to (sqrt(x-4)+1)^2 is x+2sqrt(x-4)-3

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simplify (sqrt(x-4)+1)^2

simplify

(x - 4 + 1)^{2}

x + 2 x - 4 - 3

Solution steps

(x - 4 + 1)^{2}

Apply Perfect Square Formula:

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

(x - 4 + 1)^{2} = (x - 4)^{2} + 2 x - 4 \cdot 1 + 1^{2}

= (x - 4)^{2} + 2 x - 4 \cdot 1 + 1^{2}

Simplify

(x - 4)^{2} + 2 x - 4 \cdot 1 + 1^{2} : x + 2 x - 4 - 3

= x + 2 x - 4 - 3

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