To factor the expression \( 45x - 18y + 36 \) completely, we can look for a common factor in all the terms.
The coefficients are \( 45 \), \( -18 \), and \( 36 \). The greatest common divisor (GCD) of these numbers is \( 9 \).
Now, let's factor out the \( 9 \):
\[ 45x - 18y + 36 = 9(5x - 2y + 4) \]
Next, we check if the expression \( 5x - 2y + 4 \) can be factored further. Since \( 5x \), \( -2y \), and \( 4 \) do not have a common factor, \( 5x - 2y + 4 \) is in its simplest form.
Thus, the completely factored expression is:
\[ 9(5x - 2y + 4) \]