What is the 3rd term in the expansion of (x + 4)^5? (2023)
Practice Questions
1 question
Q1
What is the 3rd term in the expansion of (x + 4)^5? (2023)
80x^3
160x^3
240x^3
320x^3
The 3rd term is given by C(5,2) * (4)^2 * (x)^3 = 10 * 16 * x^3 = 160x^3.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the 3rd term in the expansion of (x + 4)^5? (2023)
Solution: The 3rd term is given by C(5,2) * (4)^2 * (x)^3 = 10 * 16 * x^3 = 160x^3.
Steps: 8
Step 1: Identify the expression to expand, which is (x + 4)^5.
Step 2: Understand that we want 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(5, 2), which is 5! / (2!(5-2)!) = 10.
Step 6: Identify a = x and b = 4, and calculate a^(5-2) = x^3 and b^2 = 4^2 = 16.
