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### Course: High school math (India)>Unit 3

Lesson 3: Polynomials

# 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?
• If you have a different base then you can't do that. It has to be the same base.
• This probably isn't related to Distributive property or BEDMAS but can't I use FOIL for this? I'm confused :(
• 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.
• When you multiply -y(x) do you get -xy or -yx
• Usually they are put in alphabetical order, so -xy is preferred, but as said they are equivalent.
• but doesnt the rule sau you do the brackets first BEDMAS
• 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
• Can anyone please tell me on how to multiply literals which have different powers?
• 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!
• is there such thing as an apeironomial (infinite terms)?
• 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.
• do we have to add the three numbers in the end?