What is the coefficient of x^1 in the expansion of (x + 1)^10? (2021)

What is the coefficient of x^1 in the expansion of (x + 1)^10? (2021)

Step 1: Understand that we need to find the coefficient of x^1 in the expansion of (x + 1)^10.
Step 2: Recall the binomial expansion formula: (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 = 1, and n = 10.
Step 4: We want the term where x is raised to the power of 1, which means we need k = 9 (since n - k = 1).
Step 5: Calculate C(10, 1), which is the number of ways to choose 1 from 10. This is equal to 10.
Step 6: The term we are interested in is C(10, 1) * (x^1) * (1^9).
Step 7: Since (1^9) is just 1, the coefficient of x^1 is simply C(10, 1) * 1 = 10.

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