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In the expansion of (2 + 3x)^4, what is the coefficient of x?

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Question: In the expansion of (2 + 3x)^4, what is the coefficient of x?

Options:

  1. 12
  2. 24
  3. 36
  4. 48

Correct Answer: 12

Solution: 

The coefficient of x is C(4,1) * 2^3 * 3 = 4 * 8 * 3 = 96.

In the expansion of (2 + 3x)^4, what is the coefficient of x?

Practice Questions

Q1
In the expansion of (2 + 3x)^4, what is the coefficient of x?
  1. 12
  2. 24
  3. 36
  4. 48

Questions & Step-by-Step Solutions

In the expansion of (2 + 3x)^4, what is the coefficient of x?
Correct Answer: 96
  • Step 1: Identify the expression to expand, which is (2 + 3x)^4.
  • 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 = 2, b = 3x, and n = 4.
  • Step 4: We want the coefficient of x, which corresponds to the term where k = 1 (since x is to the power of 1).
  • Step 5: Calculate C(4, 1), which is the number of ways to choose 1 from 4. C(4, 1) = 4.
  • Step 6: Calculate 2^(4-1) = 2^3 = 8.
  • Step 7: Calculate (3x)^1 = 3.
  • Step 8: Multiply the results: Coefficient = C(4, 1) * 2^3 * 3 = 4 * 8 * 3.
  • Step 9: Calculate 4 * 8 = 32.
  • Step 10: Finally, calculate 32 * 3 = 96.
  • Binomial Expansion – The process of expanding expressions of the form (a + b)^n using the Binomial Theorem.
  • Coefficients in Binomial Expansion – Understanding how to find specific coefficients in the expansion, particularly for terms involving x.
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