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What is the sum of the coefficients in the expansion of (2 + 3x)^4?

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Question: What is the sum of the coefficients in the expansion of (2 + 3x)^4?

Options:

  1. 81
  2. 64
  3. 100
  4. 125

Correct Answer: 81

Solution: 

The sum of the coefficients is found by substituting x = 1: (2 + 3*1)^4 = 5^4 = 625.

What is the sum of the coefficients in the expansion of (2 + 3x)^4?

Practice Questions

Q1
What is the sum of the coefficients in the expansion of (2 + 3x)^4?
  1. 81
  2. 64
  3. 100
  4. 125

Questions & Step-by-Step Solutions

What is the sum of the coefficients in the expansion of (2 + 3x)^4?
Correct Answer: 625
  • Step 1: Identify the expression you need to expand, which is (2 + 3x)^4.
  • Step 2: To find the sum of the coefficients, substitute x = 1 into the expression.
  • Step 3: Replace x with 1 in the expression: (2 + 3*1).
  • Step 4: Calculate the value: (2 + 3*1) = (2 + 3) = 5.
  • Step 5: Now raise this result to the power of 4: 5^4.
  • Step 6: Calculate 5^4, which is 5 * 5 * 5 * 5 = 625.
  • Step 7: The final result, 625, is the sum of the coefficients.
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