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

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

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

simplify

(x - 1 + 1)^{2}

x + 2 x - 1

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

= x + 2 x - 1

\frac{100 s + 1000}{s ( s ^{2} + 10 s + 1000 )}

\frac{\partial}{\partial x} ((x - 1)^{2}) + (y - 3)^{2}

(x - 1 + 2 i) (x - 1 - 2 i)

\frac{n ( n + 1 ) ( 2 n + 1 )}{2}

(tan (x) - sec (x))^{2}