What is the sum of the coefficients in the expansion of (3x - 2)^4? (2023)

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Question: What is the sum of the coefficients in the expansion of (3x - 2)^4? (2023)

Options:

Correct Answer: 81

Exam Year: 2023

Solution:

To find the sum of the coefficients, substitute x = 1. Thus, (3(1) - 2)^4 = (3 - 2)^4 = 1^4 = 1.

What is the sum of the coefficients in the expansion of (3x - 2)^4? (2023)

What is the sum of the coefficients in the expansion of (3x - 2)^4? (2023)

Step 1: Identify the expression we need to expand, which is (3x - 2)^4.
Step 2: To find the sum of the coefficients, we substitute x = 1 into the expression.
Step 3: Substitute x = 1 into the expression: (3(1) - 2)^4.
Step 4: Calculate the expression inside the parentheses: (3 - 2) = 1.
Step 5: Now raise the result to the power of 4: 1^4.
Step 6: Calculate 1^4, which equals 1.
Step 7: The final result, which is the sum of the coefficients, is 1.

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