Evaluate: `(2a-3b)^(2)`

Answer

To evaluate the expression \((2a - 3b)^2\), we can use the formula for the square of a binomial, which states that:

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

In our case, we can identify \(x\) and \(y\) as follows:
- \(x = 2a\)
- \(y = 3b\)

Now, we can substitute these values into the formula:

1. **Calculate \(x^2\)**:
\[ x^2 = (2a)^2 = 4a^2 \]

2. **Calculate \(y^2\)**:
\[ y^2 = (3b)^2 = 9b^2 \]

3. **Calculate \(2xy\)**:
\[ 2xy = 2 \cdot (2a) \cdot (3b) = 12ab \]

Now, substituting these values into the binomial square formula:

\[ (2a - 3b)^2 = x^2 - 2xy + y^2 \]

This gives us:

\[ (2a - 3b)^2 = 4a^2 - 12ab + 9b^2 \]

Thus, the final evaluated expression is:

\[ \boxed{4a^2 - 12ab + 9b^2} \]