What is the 3rd term in the expansion of (2x + 5)^6? (2000)
Practice Questions
1 question
Q1
What is the 3rd term in the expansion of (2x + 5)^6? (2000)
600x^4
1500x^4
1800x^4
2000x^4
The 3rd term is given by C(6,2) * (2x)^2 * (5)^4 = 15 * 4 * 625 = 37500.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the 3rd term in the expansion of (2x + 5)^6? (2000)
Solution: The 3rd term is given by C(6,2) * (2x)^2 * (5)^4 = 15 * 4 * 625 = 37500.
Steps: 10
Step 1: Identify the expression to expand, which is (2x + 5)^6.
Step 2: Recognize that we need to find the 3rd term in the expansion.
Step 3: Use the binomial theorem, which states that the nth term in the expansion of (a + b)^n is given by C(n, k) * a^(n-k) * b^k, where C(n, k) is the binomial coefficient.
Step 4: For the 3rd term, we need to find k = 2 (since we start counting from k = 0).
Step 5: Calculate the binomial coefficient C(6, 2), which is the number of ways to choose 2 items from 6. This is calculated as 6! / (2!(6-2)!) = 15.
