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

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

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

simplify

(2 + x + 1)^{2}

x + 4 x + 1 + 5

Solution steps

(2 + x + 1)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= x + 4 x + 1 + 5

(3 - 1) + (3 + 1) i

\frac{( 2 s + 1 )}{s ( s + 1 ) ( s ^{2} + 4 s + 6 )}

sin (x) (csc (x) + 1) - 1

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

- \frac{( t - 1 ) ^{2}}{2}