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

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

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

simplify

(x + 1 - 2)^{2}

x - 4 x + 1 + 5

Solution steps

(x + 1 - 2)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= x - 4 x + 1 + 5

(4 + 3 i)^{5}

\frac{( 6 x - 5 ) ^{2}}{36}

(\frac{1}{p ^{2}} - 4 q)^{7}

(x^{2} + 4 i)^{2}

(1 + cos (x)) (cos (x))