What is the 5th term in the expansion of (2 + 3x)^6? (2023)

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Q: What is the 5th term in the expansion of (2 + 3x)^6? (2023)

Solution: The 5th term is given by 6C4 * (2)^(6-4) * (3x)^4 = 15 * 4 * 81x^4 = 4860x^4.

Steps: 10

Step 1: Identify the expression to expand, which is (2 + 3x)^6.
Step 2: Determine which term we want. We want the 5th term in the expansion.
Step 3: Use the formula for the nth term in the binomial expansion, which is given by nCk * (a)^(n-k) * (b)^k, where n is the exponent, k is the term number minus 1, a is the first term, and b is the second term.
Step 4: For the 5th term, we have n = 6 and k = 4 (since we start counting from 0).
Step 5: Calculate 6C4, which is the number of combinations of 6 items taken 4 at a time. This equals 15.
Step 6: Calculate (2)^(6-4), which is (2)^2 = 4.
Step 7: Calculate (3x)^4, which is (3^4)(x^4) = 81x^4.
Step 8: Multiply all the parts together: 15 * 4 * 81x^4.
Step 9: Calculate the final multiplication: 15 * 4 = 60, and then 60 * 81 = 4860.
Step 10: Combine the result with x^4 to get the final answer: 4860x^4.