Question

multiply.
(4 + \sqrt{2})(2 - 3\sqrt{10})
simplify your answer as much as possible.

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply each term in the first binomial by each term in the second binomial:
$$(4)(2) + (4)(-3\sqrt{10}) + (\sqrt{2})(2) + (\sqrt{2})(-3\sqrt{10})$$

Step2: Simplify each product

• $4\times2 = 8$
• $4\times(-3\sqrt{10}) = -12\sqrt{10}$
• $\sqrt{2}\times2 = 2\sqrt{2}$
• $\sqrt{2}\times(-3\sqrt{10}) = -3\sqrt{2\times10} = -3\sqrt{20} = -3\times2\sqrt{5} = -6\sqrt{5}$ (since $\sqrt{20} = \sqrt{4\times5} = 2\sqrt{5}$)

Step3: Combine like terms

Combine the constant term and the radical terms:
$$8 - 12\sqrt{10} + 2\sqrt{2} - 6\sqrt{5}$$

Answer:

$8 - 12\sqrt{10} + 2\sqrt{2} - 6\sqrt{5}$