Algebra (all content)
- Multiplying monomials by polynomials: area model
- Multiply monomials by polynomials: area model
- Multiplying monomials by polynomials
- Multiply monomials by polynomials
- Multiplying monomials by polynomials challenge
- Multiply monomials by polynomials challenge
- Multiplying monomials by polynomials review
Multiplying monomials by polynomials
Sal multiplies -4x² by (3x² + 25x - 7). 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?(10 votes)
- If you have a different base then you can't do that. It has to be the same base.(5 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.(5 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(5 votes)
- This probably isn't related to Distributive property or BEDMAS but can't I use FOIL for this? I'm confused :((3 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.(7 votes)
- Can anyone please tell me on how to multiply literals which have different powers?(3 votes)
- Do you mean something like:
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(7 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!(4 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:
- Quick question: how in the world are you supposed to multiply 4xsquared with another number?(3 votes)
- Is there an example of problem the is written like 3(-5x^7)x^2(3 votes)
- nah i dont think so man(2 votes)
- 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)
- What is the rule for mulitplying monomials?(2 votes)
- Are you asking about Just monomials?
If so you multiply the numbers in front of the bases together and add the exponents on the bases to get 1 term.
Hope this helps! :)(1 vote)
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.