Simplify (x- square root of 5)(x+ square root of 7)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify each term.

Multiply $x$ by $x$ .

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

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

Combine using the product rule for radicals.

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

Multiply $7$ by $5$ .

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