Multiplying Polynomials by Monomials

Multiplying Polynomials by Monomials Video

Hello! Today we’re going to take a look at how to multiply a polynomial by a monomial. Let’s start with a simple example.



When multiplying a polynomial by a monomial, you’ll want to multiply each part of the polynomial \((4x+2)\) by each part of the monomial \((3x)\). You’ll multiply the monomial, \(3x\), by the first part of the polynomial, so by this \(4x\). And then we’ll add — multiplying the monomial by this part of the polynomial, the \(+2\).



So now all we have to do is multiply each of these sets of monomials.



And that’s our answer. Not too challenging! Let’s try another one.



Remember, multiply each part of the polynomial by the monomial.



Notice that I put plus signs in between each set of multiplied terms, even though there is a –9. I did this because subtraction is always the same thing as adding a negative number. Our last sign will end up turning into a subtraction symbol, but doing it this way helps us make sure we have the correct sign attached to each term.

So now let’s multiply all of our terms. \(7y^{2}\cdot 2y^{2}=14y^{4}\). Remember, when you multiply exponential terms with the same base you simply add the exponents, so we’ve got \(2+2=4\) — so that’s where the \(y^{4}\) came from. And then, \(7y^{2}\cdot 6y=42y^{3}\), so +42y3. And then, plus \(7y^{2}\cdot (-9)=-63y^{2}\).



Remember what I said earlier? Adding a negative number is the same as subtracting, so we can rewrite this as:



Let’s try one last problem before we go.



We need to multiply each term of the polynomial by the monomial.



Now we multiply each set of monomials. Remember, a negative number times a negative number is a positive number.



We can simplify this last sign, and our final answer will be:



I hope that this video on multiplying polynomials by monomials has been helpful! Thanks for watching, and happy studying!

Return to Algebra I Videos



by Mometrix Test Preparation | This Page Last Updated: February 7, 2023