Main content

## Integrated math 3

### Course: Integrated math 3 > Unit 1

Lesson 4: Multiplying monomials by polynomials- Multiplying monomials
- Multiply monomials
- Multiplying monomials by polynomials: area model
- Area model for multiplying polynomials with negative terms
- Multiply monomials by polynomials: area model
- Multiplying monomials by polynomials
- Multiply monomials by polynomials
- Multiplying monomials by polynomials review

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Multiplying monomials by polynomials: area model

Discover how to calculate the area of complex shapes using algebra! By breaking down a rectangle into smaller parts, we can find the total area by multiplying the height and width of each part. This method introduces us to the concept of multiplying monomials by polynomials.

## Want to join the conversation?

- Is polynomials the same thing as trinomials?(6 votes)
- Trinomials are just one type of polynomial. Specifically they are a polynomial with 3 terms.

There are also monomials (1 term) and binomials (2 terms) and other polynomials that have more than 3 terms.(26 votes)

- Why are all of the videos have easy math problems? But when I do the math it's a complicated problem?(13 votes)
- The videos give you the way to solve it, and you just use it to solve the harder problems, since it has the same logic.(2 votes)

- Why are all of the videos have easy math problems? But when I do the math it's a complicated problems(4 votes)
- As long as you apply the concept/idea of the video lectures to the exercise, it's the same as any problems. The point is to understand the concept.(4 votes)

- this is sooooo confusing for me(4 votes)
- If you had an equation:

7x^2 times 3x^2 would the answer be 21x^4 or 21x^2.

Would you add the exponents together or not because they are not the same.(1 vote)- If you multiply same bases, you add the exponents, so the first answer (21x^4) is correct. If you add 7x^2 + 3x^2 = 10 x^2. When you say "they are not the same," that is not correct, the coefficients are different, but the bases ("x") are the same.(3 votes)

- What is a trinomial?

How can it relate to real-world situations?(1 vote)- A trinomial is a polynomial with three terms. Polynomials are the larger category under which you can find monomials, binomials, and trinomials.(2 votes)

- like I get it but I don’t get it at the same time haha(0 votes)
- You know how to calculate the area of a rectangle, right? It's width times height.

The height in this example would be 4. The width would be all the variables added together. So to calculate the area, the equation would be:

4(x^2 + 3x + 2)

Get rid of the brackets and you'd get:

4x^2 + 12x + 8

Hope this helps :)(3 votes)

- I get it but when I go back to my equation i don't get it like it look's easy but not at the same time.(1 vote)
- What is a trinomial?(1 vote)
- A trinomial is an algebraic expression that has three terms. If three monomials are separated by addition or subtraction, then it is a trinomial.

For example,

1 + 2x + 2x^2 or

3 + 8a + 2b(1 vote)

- Do I add the variables after solving the equation.

Ex. 24a^4+36a^3+12a^2

Do i add the variables??(1 vote)- Your polynomial is a simplified as it can be. You can only add like terms. None of the varialbes match and have matching exponents.

Hope this helps.(0 votes)

## Video transcript

- [Voiceover] We're asked
to express the area of the entire rectangle below as a trinomial. We have our rectangle here
and it's broken up into these three smaller rectangles. And we see for all of these rectangles, the height here is four
units and then the widths are expressed in terms,
or at least the first two, are expressed in terms of
x and then this last one has a width of two. So what's the area of
the entire rectangle? I encourage you to pause the
video and think about it. What's the area of this blue, this blue, it looks like a square,
but let's just call it a rectangle, which all
squares are rectangles so that's safe. Well, it's going to be the
height times the width. So the area here is
going to be the height, which is four, times the width, which is x squared. And then to that, we want
to add the area of this, I guess we could say this
salmon colored rectangle and well that's going
to be the height four times the width 3x. So we could say four times 3x, we could write it like that, but what is 4 times 3x? Well, that's going to be 12x. You have 3x four times, I have 12 xs, so that's going to be 12x. 12x is the area of this
salmon colored rectangle. And then, finally, the area
of this green rectangle, we actually can figure out
it exactly, we don't even have to express it in terms of a variable. Its height is four, its width is two, so the area's going to be
four times two, or eight. And we are done.