What is the value of the 5th term in the expansion of (x + 2)^6?
Practice Questions
Q1
What is the value of the 5th term in the expansion of (x + 2)^6?
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Questions & Step-by-Step Solutions
What is the value of the 5th term in the expansion of (x + 2)^6?
Step 1: Identify the expression we are expanding, which is (x + 2)^6.
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 = 6, and we want the 5th term, which corresponds to k = 4 (since we start counting from k = 0).
Step 5: Calculate the binomial coefficient C(6, 4). This is equal to 6! / (4! * (6-4)!) = 6! / (4! * 2!) = (6 * 5) / (2 * 1) = 15.
Step 6: Now, substitute the values into the formula: C(6, 4) * (x)^(6-4) * (2)^4 = 15 * (x)^4 * (2)^4.
