Find the square of:
`3a + 7b`

Answer

To find the square of \( 3a + 7b \), we can use the formula for the square of a binomial, which states:

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

Here, we can identify \( x = 3a \) and \( y = 7b \).

Now, let's apply the formula step by step:

1. **Identify \( x \) and \( y \)**:
- Let \( x = 3a \)
- Let \( y = 7b \)

2. **Calculate \( x^2 \)**:
\[ x^2 = (3a)^2 = 9a^2 \]

3. **Calculate \( y^2 \)**:
\[ y^2 = (7b)^2 = 49b^2 \]

4. **Calculate \( 2xy \)**:
\[ 2xy = 2 \cdot (3a) \cdot (7b) = 2 \cdot 3 \cdot 7 \cdot ab = 42ab \]

5. **Combine all parts**:
Now, substitute \( x^2 \), \( y^2 \), and \( 2xy \) back into the formula:
\[ (3a + 7b)^2 = x^2 + y^2 + 2xy = 9a^2 + 49b^2 + 42ab \]

Thus, the square of \( 3a + 7b \) is:
\[ (3a + 7b)^2 = 9a^2 + 49b^2 + 42ab \]