What is the 5th term in the expansion of (3x - 2)^6?
Practice Questions
1 question
Q1
What is the 5th term in the expansion of (3x - 2)^6?
-540x^5
540x^5
-486x^5
486x^5
The 5th term is given by C(6, 4) * (3x)^4 * (-2)^2 = 15 * 81x^4 * 4 = 4860x^4.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the 5th term in the expansion of (3x - 2)^6?
Solution: The 5th term is given by C(6, 4) * (3x)^4 * (-2)^2 = 15 * 81x^4 * 4 = 4860x^4.
Steps: 10
Step 1: Identify the expression to expand, which is (3x - 2)^6.
Step 2: Determine the term number we want, which is the 5th term.
Step 3: Use the binomial expansion formula to find the 5th term. The formula is C(n, k) * a^(n-k) * b^k, where n is the exponent, k is the term number minus 1, a is the first term, and b is the second term.
Step 4: For the 5th term, n = 6 and k = 4 (since we start counting from 0).
Step 5: Calculate C(6, 4), which is the number of combinations of 6 items taken 4 at a time. This equals 15.
Step 6: Calculate (3x)^(6-4) = (3x)^2 = 9x^2.
Step 7: Calculate (-2)^4 = 16.
Step 8: Combine these results: 15 * 9x^2 * 16.
Step 9: Multiply the numbers: 15 * 9 = 135 and then 135 * 16 = 2160.
