(a-3b)(a+2b)+5a(a+2b)

To simplify the expression \((a - 3b)(a + 2b) + 5a(a + 2b)\), we can start by factoring out the common term \((a + 2b)\):

1. Identify the common factor, which is \((a + 2b)\).
2. Rewrite the expression:

\[ = (a - 3b + 5a)(a + 2b) \]

3. Combine like terms inside the parentheses:

\[ = (6a - 3b)(a + 2b) \]

Now, we can choose to expand the expression further if needed:

\[ (6a - 3b)(a + 2b) = 6a \cdot a + 6a \cdot 2b - 3b \cdot a - 3b \cdot 2b \]

This simplifies to:

\[ = 6a^2 + 12ab - 3ab - 6b^2 \]

Combining the \(ab\) terms:

\[ = 6a^2 + 9ab - 6b^2 \]

Thus, the simplified expression is:

\[ 6a^2 + 9ab - 6b^2 \]

If you have any further questions or need additional assistance, feel free to ask!