Read the following statements carefully and select the correct option.
Statement-1 : Difference between the value of expression, `4x + 2(x + y)` when x=2, y=3 and when x=3, y = 2 is 10.
Statement-2 : `4(a + 2b) + 3b^(2) + 9ab` should be subtracted from `2a - 2b + b^(2) - 6ab` to get `- (2a + 10b + 8b^(2) + 5ab)`

Options

A. Statement-1 is true but Statement-2 is false.
B. Statement-1 is false but Statement-2 is true.
C. Both Statement-1 and Statement-2 are true.
D. Both Statement-1 and Statement-2 are false.

Answer

To solve the problem, we need to evaluate both statements and determine their validity.

### Step 1: Evaluate Statement 1
We need to find the difference between the values of the expression \(4x + 2(x + y)\) for two sets of values: \(x = 2, y = 3\) and \(x = 3, y = 2\).

1. **Substituting \(x = 2\) and \(y = 3\)**:
\[ 4(2) + 2(2 + 3) = 8 + 2(5) = 8 + 10 = 18 \]

2. **Substituting \(x = 3\) and \(y = 2\)**:
\[ 4(3) + 2(3 + 2) = 12 + 2(5) = 12 + 10 = 22 \]

3. **Finding the difference**:
\[ 22 - 18 = 4 \]

Thus, the difference is 4, not 10. Therefore, **Statement 1 is false**.

### Step 2: Evaluate Statement 2
We need to check if subtracting \(4(a + 2b) + 3b^2 + 9ab\) from \(2a - 2b + b^2 - 6ab\) results in \(- (2a + 10b + 8b^2 + 5ab)\).

1. **Write down the expressions**:
- Expression 1: \(2a - 2b + b^2 - 6ab\)
- Expression 2: \(4(a + 2b) + 3b^2 + 9ab\)

2. **Simplifying Expression 2**:
\[ 4(a + 2b) + 3b^2 + 9ab = 4a + 8b + 3b^2 + 9ab \]

3. **Subtract Expression 2 from Expression 1**:
\[ (2a - 2b + b^2 - 6ab) - (4a + 8b + 3b^2 + 9ab) \]

4. **Distributing the negative sign**:
\[ 2a - 2b + b^2 - 6ab - 4a - 8b - 3b^2 - 9ab \]

5. **Combining like terms**:
- For \(a\): \(2a - 4a = -2a\)
- For \(b\): \(-2b - 8b = -10b\)
- For \(b^2\): \(b^2 - 3b^2 = -2b^2\)
- For \(ab\): \(-6ab - 9ab = -15ab\)

Thus, we have:
\[ -2a - 10b - 2b^2 - 15ab \]

6. **Factoring out the negative sign**:
\[ - (2a + 10b + 2b^2 + 15ab) \]

Now we compare this with \(- (2a + 10b + 8b^2 + 5ab)\). The two expressions are not equal because:
- The coefficient of \(b^2\) is 2 in our result, while it is 8 in the statement.
- The coefficient of \(ab\) is 15 in our result, while it is 5 in the statement.

Therefore, **Statement 2 is also false**.

### Conclusion
Both statements are false.

### Final Answer
The correct option is that both Statement 1 and Statement 2 are false.

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