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.

## Class 9 (Foundation)

### Course: Class 9 (Foundation)>Unit 4

Lesson 3: Multiplying polynomials

# Multiplying binomials by polynomials

Learn how to multiply binomials by polynomials with ease! This lesson breaks down the process into simple steps, using the distributive property to multiply each term. You'll master combining like terms to simplify expressions, turning complex polynomials into manageable math. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• How did Sal get 50a^3 in this video? Around into the video he gets 50a^3 for his answer. Did he add the variable a and three together?
• To multiply terms with variables in them (for instance 10a times 5a^2), you have to :
1. Multiply the numerical coefficients : in this case, 10 times 5 = 50
2. Look for the same variable : in this case, a times a^2.
3. Write the variable with an exponent that is the sum of the exponents :
in this case, 1 + 2, giving a^3.
4. So the answer to 10a times 5a^2 is 50 a^3.
• Whats the hardest polynomial that anyone has encountered?
• SIMPLIFY
(2345.7647x^56 + 66t^5353)(6433x^343443)(35535t^3553+ 434x^3)
Edit: I swear, if that David guy solves this-
• Does it matter which way you FOIL out
• No, you will get the same answer despite which way you start.
(1 vote)
• Is there a faster way of doing it lol?
• Not really
But for (a + b)(c + d) where b and d are numbers
It will be a^2 + (b+d)x + (b*d)
SO, (x+3)(x+7) x^2 + 10x + 21
(1 vote)
• There is no way faster that I know of... But if you find one, Let me know! LOL
• Of course. Faster-enter the numbers in your calculator. Maybe just as good, round numbers and use scientific notation to approximate. Learning should not be a race. Life is over soon enough.
• Hey whenever Sal was doing the problem in the video and he subtracted -10a-21a how come he didn't make it -31a^2? Just wondering. :)
• he wasn't multiplying the polynomials he added them so the exponents stay the same because when you have -10 of something and -21 of something the something doesn't change.
• Wouldn't Sal need to multiply -10a by -15a^2 before trying to merge terms?
• Maybe writing out all the steps will help.

(10a-3)(5a² + 7a - 1) First he distributed the bigger set of parenthesis into the smaller set.

10a(5a² + 7a - 1) - 3(5a² + 7a - 1) Notice how the two terms are still being subtracted. In other words if (5a² + 7a - 1) was replaced with x it would look like 10ax - 3x. Now there is no multiplication between the two different parts with an x. Now do the rest of the distributions.

50a³ + 70a² - 10a - 15a² - 21a + 3 Sal showed what to do from here. the -3 was distrbuted into the right side, but the right side was being subtracted from the left, so there is no multiplication.

let me know if this did not help, I can try a different way of explaining.
• Are there other ways to solve this?
• No, not really. I mean you could do something like
(10a - 3)(5a² + 7a - 1) = (10a - 3)5a² + (10a - 3)7a - (10a - 3) = ...
or
(10a - 3)(5a² + 7a - 1) = 50a³ + 70a² - 10a - 15a² - 21a + 3 = ...,
but at the end of the day you are basically doing the same thing.
• I understand how to multiply polynomials but what about when they ask to simply an equation like this to get it's standard form:
-2 (p+4)^2 -3+5p
What are the steps to solve an equation like this?
• 1) You do not have an equation. An equation is made up on 2 expressions separated by and equals symbol. What you have is a polynomial expression.