Answer:
The correct answer is:
B. \(-5 + 2\sqrt{3}\)
Step-by-step explanation:
To evaluate the expression [tex]\((\sqrt{3} - 2)(4 + \sqrt{3})\)[/tex] using the FOIL method, we need to multiply each term in the first parenthesis by each term in the second parenthesis. The FOIL method stands for First, Outer, Inner, and Last, referring to the terms we multiply together:
1. First: Multiply the first terms in each parenthesis:
[tex]\[\sqrt{3} \times 4 = 4\sqrt{3}\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[\sqrt{3} \times \sqrt{3} = (\sqrt{3})^2 = 3\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[ -2 \times 4 = -8 \][/tex]
4. Last: Multiply the last terms:
[tex]\[-2 \times \sqrt{3} = -2\sqrt{3}\][/tex]
Now, add all these results together:
[tex]\[4\sqrt{3} + 3 - 8 - 2\sqrt{3}\][/tex]
Combine like terms (the terms with [tex]\((\sqrt{3}\))[/tex]:
[tex]\[(4\sqrt{3} - 2\sqrt{3}) + (3 - 8) = 2\sqrt{3} - 5\][/tex]
Thus, the evaluated expression is:
[tex]\[2\sqrt{3} - 5\][/tex]
Therefore, the correct answer is:
[tex]B. \(-5 + 2\sqrt{3}\)[/tex]
