Algebra Examples

$(x + \sqrt{5}) (x + \sqrt{5})$

Step 1

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

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Step 1.1

Apply the distributive property.

$x (x + \sqrt{5}) + \sqrt{5} (x + \sqrt{5})$

Step 1.2

Apply the distributive property.

$x \cdot x + x \sqrt{5} + \sqrt{5} (x + \sqrt{5})$

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ .

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

Step 2.1.2

Combine using the product rule for radicals.

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

Step 2.1.3

Multiply $5$ by $5$ .

$x^{2} + x \sqrt{5} + \sqrt{5} x + \sqrt{25}$

Step 2.1.4

Rewrite $25$ as $5^{2}$ .

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

Step 2.1.5

Pull terms out from under the radical, assuming positive real numbers.

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

Step 2.2

Reorder the factors of $\sqrt{5} x$ .

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

Step 2.3

Add $x \sqrt{5}$ and $x \sqrt{5}$ .

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