What is the 3rd term in the expansion of (x + 2)^8? (2022)

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Question: What is the 3rd term in the expansion of (x + 2)^8? (2022)

Options:

Correct Answer: 112

Exam Year: 2022

Solution:

The 3rd term is given by 8C2 * (2)^2 * (x)^6 = 28 * 4 * x^6 = 112x^6.

What is the 3rd term in the expansion of (x + 2)^8? (2022)

What is the 3rd term in the expansion of (x + 2)^8? (2022)

Step 1: Identify the expression to expand, which is (x + 2)^8.
Step 2: Understand that the 3rd term in the expansion corresponds to k = 2 (since we start counting from k = 0).
Step 3: Use the binomial coefficient formula, which is nCk = n! / (k! * (n-k)!), where n = 8 and k = 2.
Step 4: Calculate 8C2: 8! / (2! * (8-2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28.
Step 5: Calculate (2)^2, which is 4.
Step 6: Calculate (x)^(8-2), which is (x)^6.
Step 7: Combine the results: 8C2 * (2)^2 * (x)^6 = 28 * 4 * x^6.
Step 8: Multiply 28 and 4 to get 112.
Step 9: Write the final answer as 112x^6.

No concepts available.