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Find the coefficient of x^4 in the expansion of (x - 1)^5.
Find the coefficient of x^4 in the expansion of (x - 1)^5.
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Practice Questions
1 question
Q1
Find the coefficient of x^4 in the expansion of (x - 1)^5.
-5
10
-10
5
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The coefficient of x^4 is C(5,4) * (-1)^1 = 5 * (-1) = -5.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the coefficient of x^4 in the expansion of (x - 1)^5.
Solution:
The coefficient of x^4 is C(5,4) * (-1)^1 = 5 * (-1) = -5.
Steps: 8
Show Steps
Step 1: Identify the expression we need to expand, which is (x - 1)^5.
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 = x, b = -1, and n = 5.
Step 4: We want to find the term that contains x^4. This occurs when n-k = 4, which means k = 1 (since 5 - 4 = 1).
Step 5: Calculate the binomial coefficient C(5, 1), which is the number of ways to choose 1 from 5. C(5, 1) = 5.
Step 6: The term we are interested in is C(5, 1) * (x)^(5-1) * (-1)^1.
Step 7: Substitute the values: 5 * x^4 * (-1).
Step 8: The coefficient of x^4 is 5 * (-1) = -5.
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