What is the term containing x^2 in the expansion of (x + 4)^6?

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Question: What is the term containing x^2 in the expansion of (x + 4)^6?

Options:

Correct Answer: 480

Solution:

The term containing x^2 is given by C(6,2) * (4)^4 * (x)^2 = 15 * 256 * x^2 = 3840.

What is the term containing x^2 in the expansion of (x + 4)^6?

What is the term containing x^2 in the expansion of (x + 4)^6?

Step 1: Identify the expression to expand, which is (x + 4)^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 = 4, and n = 6.
Step 4: We want the term that contains x^2, which means we need k = 4 (since n - k = 2).
Step 5: Calculate C(6, 4), which is the number of ways to choose 4 from 6. This is equal to C(6, 2) = 15.
Step 6: Calculate (4)^4, which is 4 multiplied by itself 4 times. This equals 256.
Step 7: Combine the results: C(6, 4) * (4)^4 * (x)^2 = 15 * 256 * x^2.
Step 8: Calculate 15 * 256, which equals 3840.
Step 9: Therefore, the term containing x^2 in the expansion is 3840 * x^2.

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