Simplify (2x- square root of 5)( square root of x+1)

$(2 x - \sqrt{5}) (\sqrt{x} + 1)$

Expand $(2 x - \sqrt{5}) (\sqrt{x} + 1)$ using the FOIL Method.

Apply the distributive property.

$2 x (\sqrt{x} + 1) - \sqrt{5} (\sqrt{x} + 1)$

Apply the distributive property.

$2 x \sqrt{x} + 2 x \cdot 1 - \sqrt{5} (\sqrt{x} + 1)$

Apply the distributive property.

$2 x \sqrt{x} + 2 x \cdot 1 - \sqrt{5} \sqrt{x} - \sqrt{5} \cdot 1$

Simplify terms.

Simplify each term.

Multiply $2$ by $1$ .

$2 x \sqrt{x} + 2 x - \sqrt{5} \sqrt{x} - \sqrt{5} \cdot 1$

Combine using the product rule for radicals.

$2 x \sqrt{x} + 2 x - \sqrt{x \cdot 5} - \sqrt{5} \cdot 1$

Multiply $- 1$ by $1$ .

$2 x \sqrt{x} + 2 x - \sqrt{x \cdot 5} - \sqrt{5}$

Reorder factors in $2 x \sqrt{x} + 2 x - \sqrt{x \cdot 5} - \sqrt{5}$ .

$2 x \sqrt{x} + 2 x - \sqrt{5 x} - \sqrt{5}$