diviribuive law. \[ \text { (b) } 4(a+2)+6(a+3) \]

The distributive law, also known as distribution, allows us to multiply a single term by multiple terms inside parentheses. In your example, you can distribute \(4\) and \(6\) to the terms inside the parentheses: \(4(a+2)\) becomes \(4a + 8\) and \(6(a+3)\) becomes \(6a + 18\). So, combining everything, you have: \[ 4(a+2) + 6(a+3) = 4a + 8 + 6a + 18 = 10a + 26. \] Now, simplifying expressions like this is super handy in real life. Whether it's figuring out costs for supplies or calculating areas, mastering the distributive law empowers you to break down complex problems into manageable pieces. It’s like having a secret math weapon in your back pocket! Avoiding mistakes often comes down to keeping track of Signs! When distributing, be extra cautious with negative signs – they can flip the whole equation upside down if overlooked. Always double-check your terms as you distribute to ensure you stay on the right track and avoid those pesky errors.