(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!