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

The solution to (2+sqrt(1+x))^2 is x+4sqrt(1+x)+5

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

simplify

(2 + 1 + x)^{2}

x + 4 1 + x + 5

Solution steps

(2 + 1 + x)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

2^{2} + 2 \cdot 2 1 + x + (1 + x)^{2} : x + 4 1 + x + 5

= x + 4 1 + x + 5

(x^{2} + 3 x + 2) (5 x + 9 x^{2} - 2 x)

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

(4 - 4 cos (θ))^{2}

(e^{ia} - e^{- ia}) (e^{ib} + e^{- ib})

(5 - x^{3}) \cdot (2 - \frac{3}{x + 1})