What is the value of the 5th term in the expansion of (x + 2)^7?
Practice Questions
1 question
Q1
What is the value of the 5th term in the expansion of (x + 2)^7?
672
672x^4
672x^3
672x^2
The 5th term is C(7,4) * (2)^4 * x^3 = 35 * 16 * x^3 = 560x^3.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the value of the 5th term in the expansion of (x + 2)^7?
Solution: The 5th term is C(7,4) * (2)^4 * x^3 = 35 * 16 * x^3 = 560x^3.
Steps: 10
Step 1: Identify the expression we are expanding, which is (x + 2)^7.
Step 2: Understand that we want to find the 5th 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: In our case, a = x, b = 2, n = 7, and we want the 5th term. The 5th term corresponds to k = 4 (since we start counting from k = 0).
Step 5: Calculate the binomial coefficient C(7, 4). This is calculated as 7! / (4! * (7-4)!) = 7! / (4! * 3!) = 35.
Step 6: Calculate (2)^4, which is 16.
Step 7: Calculate x^(7-4), which is x^3.
Step 8: Combine these results to find the 5th term: C(7, 4) * (2)^4 * x^3 = 35 * 16 * x^3.
