What is the sum of the coefficients in the expansion of (x + 1)^8?

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Question: What is the sum of the coefficients in the expansion of (x + 1)^8?

Options:

Correct Answer: 512

Solution:

The sum of the coefficients in the expansion of (x + 1)^n is given by (1 + 1)^n = 2^n. Here, n=8, so the sum is 2^8 = 256.

What is the sum of the coefficients in the expansion of (x + 1)^8?

What is the sum of the coefficients in the expansion of (x + 1)^8?

Step 1: Identify the expression you need to expand, which is (x + 1)^8.
Step 2: Understand that the sum of the coefficients in the expansion can be found by substituting x = 1 into the expression.
Step 3: Substitute x = 1 into the expression: (1 + 1)^8.
Step 4: Simplify the expression: (1 + 1) becomes 2, so you have 2^8.
Step 5: Calculate 2^8, which equals 256.
Step 6: Conclude that the sum of the coefficients in the expansion of (x + 1)^8 is 256.

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