Question 1: The general expansion of $$ (a+b)^{\wedge} n $$ is given by: - A) $$ a^{\wedge} n+b^{\wedge} n $$ - B) $$ \Sigma k=0^{\wedge} n n k a^{\wedge} n-k b^{\wedge} k $$ - C) $$ (a+b) $$ - D) $$ a+b $$ Question 2 : In the binomial expansion of $$ (x+2)^{\wedge} 3 $$, what is the coefficient of $$ x^{\wedge} 2 $$ ? - A) 6 - B) 12 - C) 4 - D) 3 Question 3 : In the expansion

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Sure, let's address each of your questions one by one.

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**Question 1:**  
*The general expansion of $$ (a+b)^n $$ is given by:*

- **A)** $$ a^n + b^n $$
- **B)** $$ \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k $$
- **C)** $$ (a+b) $$
- **D)** $$ a+b $$

**Answer:** **B)**  
The general expansion of $$ (a+b)^n $$ is given by the **Binomial Theorem**, which states:

$$
(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
$$

Here, $$ \binom{n}{k} $$ represents the binomial coefficient, calculated as $$ \frac{n!}{k!(n-k)!} $$.

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**Question 2:**  
*In the binomial expansion of $$ (x+2)^3 $$, what is the coefficient of $$ x^2 $$?*

- **A)** 6
- **B)** 12
- **C)** 4
- **D)** 3

**Answer:** **A)** 6  
To find the coefficient of $$ x^2 $$ in the expansion of $$ (x + 2)^3 $$, we can use the Binomial Theorem:

$$
(x + 2)^3 = \sum_{k=0}^{3} \binom{3}{k} x^{3-k} (2)^k
$$

The term containing $$ x^2 $$ corresponds to $$ k = 1 $$:

$$
\binom{3}{1} x^{2} (2)^1 = 3 \times x^2 \times 2 = 6x^2
$$

So, the coefficient of $$ x^2 $$ is **6**.

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**Question 3:**  
*It seems like your third question got cut off. Could you please provide the complete question so I can assist you effectively?*

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Feel free to ask if you have any more questions or need further clarification!
**Question 1:** The general expansion of $$ (a+b)^n $$ is: - **A)** $$ a^n + b^n $$ - **B)** $$ \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k $$ - **C)** $$ (a+b) $$ - **D)** $$ a+b $$ **Answer:** **B)** **Question 2:** In the expansion of $$ (x+2)^3 $$, the coefficient of $$ x^2 $$ is: - **A)** 6 - **B)** 12 - **C)** 4 - **D)** 3 **Answer:** **A)** 6 **Question 3:** Please provide the complete question for assistance. **Summary:** - **Question 1:** The correct expansion is the Binomial Theorem (Option B). - **Question 2:** The coefficient of $$ x^2 $$ in $$ (x+2)^3 $$ is 6 (Option A). - **Question 3:** Additional information is needed to answer the question.

Question 1: The general
expansion of is given
by:

A)

B)

C)

D)
Question 2 : In the binomial
expansion of , what is
the coefficient of ?

A) 6

B) 12

C) 4

D) 3
Question 3 : In the expansion

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Question 1: The general expansion of is given by: A) B) C) D) Question 2 : In the binomial expansion of , what is the coefficient of ? A) 6 B) 12 C) 4 D) 3 Question 3 : In the expansion