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

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

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

simplify

(x + 1 + 1)^{2}

x + 2 x + 1 + 2

Solution steps

(x + 1 + 1)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= x + 2 x + 1 + 2

- \frac{( x + 1 ) ^{2}}{2}

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