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### Course: Algebra (all content)>Unit 10

Lesson 8: Multiplying binomials by polynomials

# Multiplying binomials by polynomials: area model

Discover the magic of multiplying binomials by polynomials using an area model! This method transforms complex algebra into simple rectangles, making it easier to understand. By breaking down the big rectangle into smaller ones, we can find the area and thus the product of the polynomials.

## Want to join the conversation?

• If there are monomials, binomials, trinomials, then are there quanomials or quinomials?
• I think past trinomials they're just referred to as polynomials.
• Why do we have to learn math that were never probally never use in the real world?
• For everyone who is asking the same question (i guess Marlon is way past this anyway)...
1. If you plan on studying any STEM subject, you will need this. Period.
2. Also it's quite possible that you will need it in any advanced form of business, banking or insurance work.
3. Even if you will never encounter a wild polynomial of the 3rd degree, going through this helps you think in a different way, use your brain and train it to push itself.
It's the same with historic dates, the fine arts, music, PE, languages. It all shapes your brain to be used in different ways.
Think about it as crossfit for your head. I guess no one needs to do push ups, squats or ride a bike real fast in the real world, but it all helps to keep your body functioning at a high level and keeps you healthy.

I know school sometimes lacks any real world application, but becoming smarter through training can help you make a living in the long run.

And one more thing, don't believe everything you think right now. Don't fall into the trap to let your 14, 16, 22 year old self limit your future options. I am 38 right now and decided to study Artificial Intelligence, but if you had asked me 20 years ago, I would have told you, I will never work in any field which requires math. ;)
• Isn't this method also called the box method??
• I prefer calling it the box method because, to me at least, this is a way of organizing in specific categories (in this case, terms), and boxes are also helpful to categorize stuff so it's easier later when you need them!
• So the only reason the expression -6y & -2y can represent a length because there are two terms? If there were only one term either( -6 or -y) & (-2 or -y) would this logic be applicable? My instincts tell me that there needs to be another variable to mulitply by the negative to give us a positive. Am I correct in thinking this?
• What I understood was that you are thinking that if you have only one term (like -6y), it would not be able to represent a distance. This is incorrect. I'll write the different ways to represent distance.

-6 = Not able to represent distance because it is just a negative number by itself and you can't have negative distances.

-y = Can represent a distance if y is also negative so if y was -3, it would represent -(-3) or 3.

-6y = Also can represent distance, if y is also negative. If y was -3, it would represent -6(-3) or 18.

-6*-y = Also can represent distance, if y is positive. If y was 3, it would be (-6)(-3) or 18.

y^2 = If y is negative or positive, it would represent distance.

y^3 = if y was positive, it could represent a distance.

So, you don't need two terms to represent distance, there are just some assumptions you have to make if you ever come across a problem like this one.
• QUESTION

Is there an easier way to do this? like a simple formula? thanks! :D
• I accidentally posted a comment, but if any other people have the same question,

I do not believe that there are any formulas related to the product of a binomial and a polynomial. Distributing and collecting like terms is the simplest way to find the product.
• How do you multiply a binomial area model? and what is the definition of binomial in math?
(1 vote)
• A binomial is a polynomial with two terms.
• I don't understand. Can someone please clarify this? are the exponents supposed to go from largest to smallest or smallest to largest??!!
• Greatest to least. For example it'd be x^4-x^3-x^2.
• This was going way too fast, how do I SLOW it down?
-Chuy
(1 vote)
• In the lower right portion of the video window, you should see a gear symbol. If you select it, there are options for changing the video speed.

Also, remember that you can pause the video when you start to get confused. You can back if up a little bit or read the transcript to pick up words that you might have missed. Then, resume playing the video.