Algebra Examples

$(x - \sqrt{5}) (x + \sqrt{7})$

Step 1

Expand $(x - \sqrt{5}) (x + \sqrt{7})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x (x + \sqrt{7}) - \sqrt{5} (x + \sqrt{7})$

Step 1.2

Apply the distributive property.

$x \cdot x + x \sqrt{7} - \sqrt{5} (x + \sqrt{7})$

Step 1.3

Apply the distributive property.

$x \cdot x + x \sqrt{7} - \sqrt{5} x - \sqrt{5} \sqrt{7}$

Step 2

Simplify each term.

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Step 2.1

Multiply $x$ by $x$ .

$x^{2} + x \sqrt{7} - \sqrt{5} x - \sqrt{5} \sqrt{7}$

Step 2.2

Multiply $- \sqrt{5} \sqrt{7}$ .

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Step 2.2.1

Combine using the product rule for radicals.

$x^{2} + x \sqrt{7} - \sqrt{5} x - \sqrt{7 \cdot 5}$

Step 2.2.2

Multiply $7$ by $5$ .

$x^{2} + x \sqrt{7} - \sqrt{5} x - \sqrt{35}$