Question

multiply and simplify.

\\(3 - 6\sqrt{7})(6 + 2\sqrt{7})\\

\\(3 - 6\sqrt{7})(6 + 2\sqrt{7}) = \square\\
(type an exact answer, using radicals as needed.)

Explanation:

⚡ Using what you learned: Roots and Radicals

Step 1: Distribute the terms

Apply the FOIL method to multiply the two binomial expressions:

$$ (3 - 6\sqrt{7})(6 + 2\sqrt{7}) = (3)(6) + (3)(2\sqrt{7}) - (6\sqrt{7})(6) - (6\sqrt{7})(2\sqrt{7}) $$

Step 2: Multiply each pair

Calculate the product of each term:

$$ 18 + 6\sqrt{7} - 36\sqrt{7} - 12(\sqrt{7})^2 $$

$$ 18 + 6\sqrt{7} - 36\sqrt{7} - 12(7) $$

$$ 18 + 6\sqrt{7} - 36\sqrt{7} - 84 $$

Step 3: Combine like terms

Group the constant terms and the radical terms together:

$$ (18 - 84) + (6\sqrt{7} - 36\sqrt{7}) $$

$$ -66 - 30\sqrt{7} $$

Answer:

$$ -66 - 30\sqrt{7} $$