In the expansion of (2x + 3)^4, what is the coefficient of x^1?

In the expansion of (2x + 3)^4, what is the coefficient of x^1?

Correct Answer: 216

Step 1: Identify the expression to expand, which is (2x + 3)^4.
Step 2: Recognize that we need to find the coefficient of x^1 in the expansion.
Step 3: Use the Binomial Theorem, which states that (a + b)^n = Σ (C(n, k) * a^(n-k) * b^k) for k = 0 to n.
Step 4: In our case, a = 2x, b = 3, and n = 4.
Step 5: We want the term where x has an exponent of 1, which means we need to find the term where (2x) is raised to the power of 1.
Step 6: This means we need to find the term where k = 3 (since n - k = 1).
Step 7: Calculate C(4, 3), which is the number of ways to choose 3 from 4. C(4, 3) = 4.
Step 8: Calculate (2)^1, which is 2.
Step 9: Calculate (3)^3, which is 27.
Step 10: Multiply these values together: 4 (from C(4, 3)) * 2 (from (2)^1) * 27 (from (3)^3).
Step 11: The final calculation is 4 * 2 * 27 = 216.

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