What is the value of the 3rd term in the expansion of (x + 2)^5?

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Question: What is the value of the 3rd term in the expansion of (x + 2)^5?

Options:

Correct Answer: 40

Solution:

The 3rd term in the expansion of (x + 2)^5 is C(5, 2)(x)^2(2)^3 = 10 * x^2 * 8 = 80.

What is the value of the 3rd term in the expansion of (x + 2)^5?

What is the value of the 3rd term in the expansion of (x + 2)^5?

Step 1: Identify the expression to expand, which is (x + 2)^5.
Step 2: Use the Binomial Theorem, which states that (a + b)^n = Σ [C(n, k) * a^(n-k) * b^k] for k = 0 to n.
Step 3: In our case, a = x, b = 2, and n = 5.
Step 4: We want the 3rd term in the expansion. The 3rd term corresponds to k = 2 (since we start counting from k = 0).
Step 5: Calculate C(5, 2), which is the number of combinations of 5 items taken 2 at a time. C(5, 2) = 5! / (2!(5-2)!) = 10.
Step 6: Calculate (x)^(5-2) = (x)^3 = x^3.
Step 7: Calculate (2)^2 = 2^2 = 4.
Step 8: Combine these results to find the 3rd term: C(5, 2) * (x)^3 * (2)^2 = 10 * x^3 * 4.
Step 9: Multiply the coefficients: 10 * 4 = 40.
Step 10: Therefore, the 3rd term in the expansion of (x + 2)^5 is 40x^3.

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