What is the value of the term containing x^5 in the expansion of (x + 2)^8? (202

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Question: What is the value of the term containing x^5 in the expansion of (x + 2)^8? (2020)

Options:

Correct Answer: 128

Solution:

The term containing x^5 is C(8,5)(2)^3 = 56 * 8 = 448.

What is the value of the term containing x^5 in the expansion of (x + 2)^8? (2020)

What is the value of the term containing x^5 in the expansion of (x + 2)^8? (2020)

Step 1: Identify the expression to expand, which is (x + 2)^8.
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 = 8.
Step 4: We want the term that contains x^5. This means we need to find the term where the exponent of x is 5.
Step 5: If x has an exponent of 5, then 2 must have an exponent of (8 - 5) = 3.
Step 6: The term we are looking for is given by C(8, 5) * (x^5) * (2^3).
Step 7: Calculate C(8, 5), which is the number of combinations of 8 items taken 5 at a time. C(8, 5) = 56.
Step 8: Calculate 2^3, which is 2 * 2 * 2 = 8.
Step 9: Multiply the results: 56 (from C(8, 5)) * 8 (from 2^3) = 448.
Step 10: The value of the term containing x^5 in the expansion is 448.

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