Get the information you need quickly and easily with IDNLearn.com. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.
Sagot :
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]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.