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If the Binomial Theorem is applied to (x + 2)^4, what is the term containing x^2
If the Binomial Theorem is applied to (x + 2)^4, what is the term containing x^2?
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Practice Questions
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Q1
If the Binomial Theorem is applied to (x + 2)^4, what is the term containing x^2?
12x^2
24x^2
36x^2
48x^2
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The term containing x^2 is C(4,2) * x^2 * 2^2 = 6 * x^2 * 4 = 24x^2.
Questions & Step-by-step Solutions
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Q
Q: If the Binomial Theorem is applied to (x + 2)^4, what is the term containing x^2?
Solution:
The term containing x^2 is C(4,2) * x^2 * 2^2 = 6 * x^2 * 4 = 24x^2.
Steps: 9
Show Steps
Step 1: Identify the expression we are working with, which is (x + 2)^4.
Step 2: Recognize that we need to find the term that contains x^2.
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 = x, b = 2, and n = 4.
Step 5: We want the term where x has the power of 2, which means we need k = 2 (because x^(n-k) = x^2).
Step 6: Calculate n - k, which is 4 - 2 = 2. This means we will use b^2, which is 2^2.
Step 7: Calculate the binomial coefficient C(4, 2), which is 4! / (2! * (4-2)!) = 6.
Step 8: Now, combine everything: the term is C(4, 2) * x^2 * 2^2 = 6 * x^2 * 4.
Step 9: Simplify the expression: 6 * 4 = 24, so the term is 24x^2.
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