Find the coefficient of x^4 in the expansion of (x + 2)^6.

Find the coefficient of x^4 in the expansion of (x + 2)^6.

Step 1: Identify the expression to expand, which is (x + 2)^6.
Step 2: 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 3: In our case, a = x, b = 2, and n = 6.
Step 4: We want the term where x has the power of 4, which means we need to find the term where k = 2 (since 6 - k = 4).
Step 5: Calculate C(6, 2), which is the number of ways to choose 2 from 6. C(6, 2) = 6! / (2!(6-2)!) = 15.
Step 6: Calculate (2)^2, which is 4.
Step 7: Multiply the results from Step 5 and Step 6: 15 * 4 = 60.
Step 8: The coefficient of x^4 in the expansion of (x + 2)^6 is 60.

Binomial Expansion – The process of expanding expressions of the form (a + b)^n using the binomial theorem.
Combination Formula – Understanding how to calculate combinations, denoted as C(n, k), which represents the number of ways to choose k elements from a set of n elements.
Coefficient Extraction – Identifying and calculating the specific coefficient of a term in a polynomial expansion.