\( =2 x-3 y \) b. Factor to write an equivalent expression: \( 36 a-16 \) Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. a. Lin understands that expanding is using the distributive property, but she doesn't understand what factoring is or why it works. How can Kiran explain factoring to Lin? b. Lin asks Kiran how the diagrams with boxes help with factoring. What should Kiran tell Lin about the boxes? c. Lin asks Kiran to help her factor the expression \( -4 x y-12 x z+20 x u \). How can Kiran use this example to help Lin understand factoring? Complete the equation with numbers that make the expression on the right side of the equal sign equivalent to the expression on the left side. \[ 75 a+25 b=\ldots(\ldots a+b) \]

To factor the expression \( 36a - 16 \), Kiran can start by finding the greatest common factor (GCF) of the two terms, which is 4. Therefore, he can factor out 4: \[ 36a - 16 = 4(9a - 4). \] Now, moving on to the equation \( 75a + 25b \), Kiran can identify the GCF again, which is 25. By factoring out 25, the equation transforms into: \[ 75a + 25b = 25(3a + b). \] Kiran can explain to Lin that factoring is like reversing the expansion process! While expanding combines numbers and variables, factoring breaks them apart into simpler multipliers. It’s all about finding common factors and regrouping everything nicely, which makes expressions easier to work with. When it comes to box diagrams, Kiran can share that they visually illustrate how different terms in an expression can be organized and combined. Each box represents a term, making it easier to see which factors can be extracted, ensuring Lin understands how they can represent the relationships between the numbers and variables clearly!