If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Algebra 2>Unit 1

Lesson 4: Multiplying monomials by polynomials

# Multiplying monomials

Learn how to multiply monomials like a pro! Discover how to multiply numbers and variables separately, then combine them for the final answer. Explore how exponent properties come into play when multiplying variables. Dive into examples with different variables for variety.

## Want to join the conversation?

• At , I would like to make sure that I have the correct answer for the "cliffhanger". Is it 20x^9
Thanks
• Yes, you have the correct answer. Good job. Looks like they cut the video off too quickly.
• Why are the exponents not multiplied?
• x^a * x^b = x^a+b
If you have 2^2 * 2^3 the correct answer is 32. If you multiplied the exponents you would get 64. Hope that explains it.
• If you did something like 5x^7 * 5x^4 you would get 25x^11. However, in the video he did 5^2 * 5^4 and got 5^6. Why did he not multiply the co-efficients?
• Because the coefficient in the latter case is 1. Imagine multiplying x^2*x^4, then substitute x=5
• At , The answer for the problem 5x^4 * 4x^6 should be 20x^9 not 9x^18.
• At , Sal clearly tells you that he is going to show you a wrong answer. He is showing common errors that students make to try and help you avoid them.

And, FYI... your version: 5x^4 * 4x^6 = 20x^10, not 20x^9
Sal's problem: 5x^3 * 4x^6 does equal 20x^9
• I understand that multiplying the same base the base does not change, but what if one of the bases is positive and the other negative? i.e. a base of -7 and 7. Does it become -49?
• Exponents represent multiplication of a common base value. If the bases are not the same, then exponent properties don't apply. In certain cases, you may be able to clean up the signs to force a common base. For example: (-7)^2 = 7^2. So, if you had (-7)^2 * 7^3, you can simplify this to: 7^2 * 7^3 = 7^5

• ok so in my math class we are multiplying, dividing, adding, and subtracting monomials. but exactly how do we find out what the answer will be if all the problems are related to polynomials? what even are polynomials?
• polynomials are a series of monomials that are added or subtracted together. There are a few extra rules though. The powers of the variables must be positive whole numbers, so no negative powers and no fractions or decimals as powers. Also coefficients can be fractons or decimals, but if there is a variable in a denominator then it is not a polynomial any more.

Technically monomials, binomials and trinomials are all kinds of polynomials. Also, if you have two terms in a polynomial that have the same variable to the same power, you need to combine it. so 5x^2 + 3x^2 would be 8x^2

As for how to solve them that is almost half a school year's worth of explanation. it will all be addressed on the site though.

One concept that is invaluable is this. All polynomials can be written as a series of binomials multiplied together. so something like (x+2)(x-1) and so on. You will learn how to write them like this. But you really want to know how to solve them when they are like this.

you will almost always have them equal to 0. so (x+2)(x-1) = 0

When you have this what happens if x was -2 or 1? well let's see.

if x was -2 then (x+2)(x-1) = (-2+2)(-2-1) = 0*-3 = 0.

Similarly if x = 1 then (x+2)(x-1) = 3*0 = 0.

So when you have the binomials multiplied together you just need to remember that the answers are when each binomial is 0.

ANother quick example. (x+2)(x-3)(x-5)(x-7) = 0 would have the answers -2, 3, 5 and 7.

You should learn how to do all this as you go, but consider this a head start
• is it me, or do all his 5s look like Ss?
• they just happen to look similar. Each person has their own handwriting so each to their own I guess :)