What is the 3rd term in the expansion of (x + 3)^4? (2023)
Practice Questions
1 question
Q1
What is the 3rd term in the expansion of (x + 3)^4? (2023)
36x^2
54x^2
72x^2
108x^2
The 3rd term is C(4,2) * (3)^2 * (x)^2 = 6 * 9 * x^2 = 54x^2.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the 3rd term in the expansion of (x + 3)^4? (2023)
Solution: The 3rd term is C(4,2) * (3)^2 * (x)^2 = 6 * 9 * x^2 = 54x^2.
Steps: 10
Step 1: Identify the expression to expand, which is (x + 3)^4.
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 (x + 3)^4, we have n = 4, a = x, and b = 3.
Step 5: The 3rd term corresponds to k = 2 (since we start counting from k = 0).
Step 6: Calculate the binomial coefficient C(4, 2), which is 4! / (2! * (4-2)!) = 6.
Step 7: Calculate (3)^2, which is 9.
Step 8: Calculate (x)^2, which is x^2.
Step 9: Combine these results to find the 3rd term: C(4, 2) * (3)^2 * (x)^2 = 6 * 9 * x^2.
Step 10: Multiply 6 and 9 to get 54, so the 3rd term is 54x^2.
