Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $2$ by $1$ .

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

Step 2.1.2

Combine using the product rule for radicals.

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

Step 2.1.3

Multiply $- 1$ by $1$ .

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

Step 2.2

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

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