What is the 5th term in the expansion of (3x - 2)^7? (2023)
Practice Questions
1 question
Q1
What is the 5th term in the expansion of (3x - 2)^7? (2023)
-1680x^3
1680x^3
-2520x^3
2520x^3
The 5th term is given by C(7,4) * (3x)^4 * (-2)^3 = 35 * 81 * (-8) = -1680x^3.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the 5th term in the expansion of (3x - 2)^7? (2023)
Solution: The 5th term is given by C(7,4) * (3x)^4 * (-2)^3 = 35 * 81 * (-8) = -1680x^3.
Steps: 11
Step 1: Identify the expression to expand, which is (3x - 2)^7.
Step 2: Determine the term number we want, which is the 5th term.
Step 3: Use the formula for the k-th term in the binomial expansion: T(k) = C(n, k-1) * (a)^(n-k+1) * (b)^(k-1), where n is the exponent, a is the first term, b is the second term, and C(n, k-1) is the binomial coefficient.
Step 4: For the 5th term, k = 5, so we need C(7, 4) * (3x)^(7-4) * (-2)^(4).
Step 5: Calculate the binomial coefficient C(7, 4), which is 7! / (4! * (7-4)!) = 35.
