What is the 3rd term in the expansion of (2x + 3)^4?
Practice Questions
Q1
What is the 3rd term in the expansion of (2x + 3)^4?
108x^2
216x^2
324x^2
432x^2
Questions & Step-by-Step Solutions
What is the 3rd term in the expansion of (2x + 3)^4?
Step 1: Identify the expression to expand, which is (2x + 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 (2x + 3)^4, we have n = 4, a = 2x, 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 (2x)^(4-2) = (2x)^2 = 4x^2.
Step 8: Calculate 3^2 = 9.
Step 9: Combine these results: 6 * 4x^2 * 9.
Step 10: Multiply: 6 * 4 = 24, and then 24 * 9 = 216.
Step 11: Therefore, the 3rd term in the expansion is 216x^2.
