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What is the coefficient of x^5 in the expansion of (x + 2)^7?

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Question: What is the coefficient of x^5 in the expansion of (x + 2)^7?

Options:

  1. 21
  2. 42
  3. 35
  4. 28

Correct Answer: 35

Solution: 

The coefficient of x^5 is C(7,5)(2)^2 = 21 * 4 = 84.

What is the coefficient of x^5 in the expansion of (x + 2)^7?

Practice Questions

Q1
What is the coefficient of x^5 in the expansion of (x + 2)^7?
  1. 21
  2. 42
  3. 35
  4. 28

Questions & Step-by-Step Solutions

What is the coefficient of x^5 in the expansion of (x + 2)^7?
Correct Answer: 84
  • Step 1: Identify the expression we need to expand, which is (x + 2)^7.
  • 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 = 7.
  • Step 4: We want the term where x is raised to the power of 5, which means we need to find the term where k = 2 (because 7 - k = 5).
  • Step 5: Calculate C(7, 2), which is the number of ways to choose 2 from 7. C(7, 2) = 7! / (2!(7-2)!) = 21.
  • Step 6: Calculate 2^2, which is 4.
  • Step 7: Multiply the results from Step 5 and Step 6: 21 * 4 = 84.
  • Step 8: The coefficient of x^5 in the expansion of (x + 2)^7 is 84.
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