Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up.
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?
Lin asks Kiran how the diagrams with boxes help with factoring. What should Kiran tell Lin about the boxes?
Lin asks Kiran to help her factor the expression -4xy−12xz+20xw. How can Kiran use this example to Lin understand factoring?
Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up.
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?
Lin asks Kiran how the diagrams with boxes help with factoring. What should Kiran tell Lin about the boxes?
Lin asks Kiran to help her factor the expression -4xy−12xz+20xw. How can Kiran use this example to Lin understand factoring?
Answers
Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up.
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?
Lin asks Kiran how the diagrams with boxes help with factoring. What should Kiran tell Lin about the boxes?
Lin asks Kiran to help her factor the expression -4xy−12xz+20xw. How can Kiran use this example to Lin understand factoring?
Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up.
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?
Lin asks Kiran how the diagrams with boxes help with factoring. What should Kiran tell Lin about the boxes?
Lin asks Kiran to help her factor the expression -4xy−12xz+20xw. How can Kiran use this example to Lin understand factoring?
To explain factoring to Lin, Kiran can start by giving her an example of expanding and then show her how to reverse the process using factoring.
For instance, if they start with the expression (2x + 3)(4x - 5) and expand it using the distributive property, they get 8x² - 2x - 15.
Kiran can then explain that factoring is simply the opposite of expanding, where instead of multiplying two expressions, we break down a given expression into simpler factors.
Regarding the boxes, Kiran can tell Lin that the boxes help to visually represent the distributive property, making it easier to understand. By drawing a box and dividing it into smaller boxes or rectangles, they can see how the expression inside the box can be broken down into simpler factors. Each box represents a factor, and the sum of the boxes represents the expanded expression.
To help Lin factor the expression -4xy - 12xz + 20xw, Kiran can begin by looking for common factors. In this case, they can factor out -4x, which gives:
-4x(y + 3z - 5w)
Now, the expression has been simplified into a product of two factors. Kiran can explain to Lin that this is the essence of factoring: breaking down a complex expression into simpler factors. They can also check their answer by expanding the expression using the distributive property and verifying that it is equal to the original expression.
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