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## Get ready for Precalculus

### Course: Get ready for Precalculus>Unit 2

Lesson 2: Multiplying binomials by polynomials

# Multiplying binomials by polynomials: area model

Sal expresses the area of a rectangle whose height is y²-6y and width is 3y²-2y+1.

## 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. ;)
• 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.
• when sal is adding -18y3 and-2y3 why doesn't he add up the exponents so it equals -20y6 instead of -20y3?
(1 vote)
• Exponents represent repetitive multiplication. You would need y^3 times y^3 to get y^6.

When combining like terms, we only add/subtract the coefficients of the variables. The variables themselves do not change.

Hope this helps.
• At , we knew that the two equations are the same but how do you factorize 3y^4 - 20y ^3 +13y^2 - 6y into (y^2 - 6y)(3y^2 -2y+1)?
• Isn't this method also called the box method??
• Are we adding or multiplying the exponents? I'm confused.
• When each product is calculated to get a term, the exponents are being added.

Recall that when multiplying expressions using the same base, add the exponents.

If you forget this rule, try a simple example such as x^2 * x^3 using the basic definition of exponents:
x^2 * x^3 = (x*x)*(x*x*x) = x*x*x*x*x = x^5.

Note that 2 and 3 are added, not multiplied, to get the 5.
(1 vote)
• can this be done with other shapes?