Question

multiply:

1. $(8 - 3sqrt{5})(2 + 4sqrt{5})$

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
\(8\times2 + 8\times4\sqrt{5}-3\sqrt{5}\times2 - 3\sqrt{5}\times4\sqrt{5}\)

Step2: Simplify each product

Calculate each term:
\(16 + 32\sqrt{5}-6\sqrt{5}-12\times5\) (since \(\sqrt{5}\times\sqrt{5}=5\))

Step3: Combine like terms

Combine the constant terms and the radical terms:
\(16 - 60+(32\sqrt{5}-6\sqrt{5})\)
\(-44 + 26\sqrt{5}\)

Answer:

\(-44 + 26\sqrt{5}\)