What is (1+sqrt(x+4))^2 ?

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

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simplify (1+sqrt(x+4))^2

simplify

(1 + x + 4)^{2}

x + 2 x + 4 + 5

Solution steps

(1 + x + 4)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= x + 2 x + 4 + 5

\frac{5 s}{( s ^{2} + 4 ) ( s ^{2} + 5 s + 4 )}

x (x^{4} e^{6 x} + 5)

- \frac{2 ( x + 1 )}{x + 4}

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

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