Find the square of `(2x+3y)`

Options

A. Statement -1 is true, Statement -2 is true, Statement -2 is a correct explanation for Statement-1
B. Statement -1 is true, Statement -2 is true, Statement -2 is not a correct explanation for Statement -1
C. Statement -1 is true, Statement -2 is false
D. Statement -1 is false, Statement -2 is true

Explanation

To find the square of \( (2x + 3y) \), we can use the algebraic identity for the square of a binomial. The identity states:

\[ (a + b)^2 = a^2 + b^2 + 2ab \]

In our case, we can let:
- \( a = 2x \)
- \( b = 3y \)

Now, we can apply the formula step by step.

### Step 1: Identify \( a \) and \( b \)
Here, we have:
- \( a = 2x \)
- \( b = 3y \)

### Step 2: Apply the formula
Using the formula \( (a + b)^2 = a^2 + b^2 + 2ab \), we can substitute \( a \) and \( b \):

\[ (2x + 3y)^2 = (2x)^2 + (3y)^2 + 2(2x)(3y) \]

### Step 3: Calculate \( a^2 \)
Calculate \( (2x)^2 \):

\[ (2x)^2 = 4x^2 \]

### Step 4: Calculate \( b^2 \)
Calculate \( (3y)^2 \):

\[ (3y)^2 = 9y^2 \]

### Step 5: Calculate \( 2ab \)
Calculate \( 2(2x)(3y) \):

\[ 2(2x)(3y) = 2 \cdot 2 \cdot 3 \cdot xy = 12xy \]

### Step 6: Combine the results
Now, combine all the results together:

\[ (2x + 3y)^2 = 4x^2 + 9y^2 + 12xy \]

Thus, the final answer is:

\[ (2x + 3y)^2 = 4x^2 + 9y^2 + 12xy \]

---