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### Course: Algebra 2 > 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

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# Multiplying monomials by polynomials

Discover how to multiply monomials by polynomials using the distributive property. Learn to simplify expressions by multiplying coefficients and adding exponents. Get a handle on negative terms and see how they affect the final result. It's all about breaking down complex problems into simpler steps! Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- We add the exponents when we have the same base, what about if we have a different base?(12 votes)
- If you have a different base then you can't do that. It has to be the same base.(10 votes)

- This probably isn't related to Distributive property or BEDMAS but can't I use FOIL for this? I'm confused :((5 votes)
- FOIL is used when you are multiplying 2 binomials. In the video, the problems involve multiplying a monomial with a polynomial, which just uses the distributive property.(12 votes)

- When you multiply -y(x) do you get -xy or -yx(4 votes)
- Usually they are put in alphabetical order, so -xy is preferred, but as said they are equivalent.(8 votes)

- but doesnt the rule sau you do the brackets first BEDMAS(5 votes)
- He is! and the only way you can take away the brackets, (the P in PEMDAS (you spelled it wrong))

is multiplying out the terms in the brackets by the outside number, but the thing is, the brackets are for that! FOR EXAMPLE!

4x(3x + 45 - 4y)

the parentheses mean to multiply everything inside by the outside number so to clear up confusion...

6(8x - 9)

is the same as...

6 times 8x - 9

hope this helped! :D(6 votes)

- Can anyone please tell me on how to multiply literals which have different powers?(3 votes)
- Do you mean something like:
`5x^2y (7x^3y^5)`

?

If yes, here are the steps:

1) Regroup - multiply number to number, X to X and Y to X:

`(5 * 7) (x^2 * x^3) (y * y^5)`

2) To multiply the X's and the Y's, you use the properties of exponents (add the exponents).

`(5 * 7) (x^2 * x^3) (y * y^5)`

=`35 x^(2+3) y^(1+5)`

=`35 x^5 y^6`

To review working with exponents, see the lesson at this link: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/v/exponent-properties-involving-products(8 votes)

- I don't know if this is the right place to ask, but what is monomial and polynomials? I looked it up but the definitions and examples are not very precise. Please help!(3 votes)
- nah it's cool it's still good practicing higher level or not,

Monomials are polynomials, but polynomials are not always monomials.**Polynomials**are terms that have constants, variables, or both.**Monomials**are polynomials that have only one term, hence the prefix "mono".

I reccomend this video for building a good foundation of what they are:

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:multiply-monomial-polynomial/v/polynomials-intro(3 votes)

- is there such thing as an apeironomial (infinite terms)?(3 votes)
- I've never heard of "apolynomial" before. You
*could*theoretically have a polynomial with infinite terms, but I'm not aware of any names it may have, or if it's even considered a polynomial at that point.

Maybe something like`f(x) = 1 + x + x^2 + x^3 + x^4 + ...`

is a simplest example!

These 'infinite polynomials' can behave in very unique ways. But this quickly leads to*calculus*so don't worry about it...

Happy learning.(2 votes)

- do we have to add the three numbers in the end?(3 votes)
- no you do not(1 vote)

- How did he get the +'s in between the ( ) inthe first one he did, which is the one below the problem...(3 votes)
- He was putting parts of the equations in parentheses. To finish the equation he needs to add the equations in the parentheses.(1 vote)

- Quick question: how in the world are you supposed to multiply 4xsquared with another number?(2 votes)

## Video transcript

Multiply negative 4x squared
by the whole expression 3x squared plus 25x minus 7. So if you multiply anything
times a whole expression, you really just use the
distributive property to multiply each term
of the expression by the negative 4x squared. So we're going to
have to distribute this negative 4x squared over
every term in the expression. So first, we could
start with negative 4x squared times 3x squared. So we can write that. We're going to have negative
4x squared times 3x squared. And to that, we're going to add
negative 4x squared times 25x. And to that, we're going
to add negative 4x squared times negative 7. So let's just simplify
this a little bit. Now, we can obviously
swap the order. We're just multiplying
negative 4 times x squared times 3
times x squared. And actually, I'll
do out every step. Eventually, you can do
some of this in your head. This is the exact same thing
as negative 4 times 3 times x squared times x squared. And what is that equal to? Well, negative 4 times
3 is negative 12. And x squared times x
squared-- same base. We're taking the product. That's going to be
x to the fourth. So this right here is
negative 12x to the fourth. Now let's think about
this term over here. This is the same thing
as-- and of course, we have this plus out here. And then this part right
here is the exact same thing as 25 times negative 4
times x squared times x. So let's just multiply
the numbers out here. These were the coefficients. 25 times negative
4 is negative 100. So it'll plus negative
100, or we could just say it's minus 100. And then we have
x squared times x, or x squared times x
to the first power. Same base-- we can
add the exponents. 2 plus 1 is 3. So this is negative
100x to the third power. And then let's look at
this last term over here. We have negative 4x squared. So this is going
to be plus-- that's this plus right over here. We have negative 4. We can multiply that
times negative 7. And then multiply
that times x squared. I'm just changing the order
in which we multiply it. So negative 4 times
negative 7 is positive 28. And then I'm going to multiply
that times the x squared. There's no simplification
to do, no like terms. These are different powers of x. So we are done.