Course Navigator
Back To Course
Math 101: College Algebra11 chapters | 81 lessons
As a member, you'll also get unlimited access to over
Kathryn teaches college math. She holds a master's degree in Learning and Technology.
Multiplication and division of rational polynomial expressions is easy once you remember the steps.
For multiplication: factor, cancel or slash, and multiply.
For division: factor, flip, cancel or slash, and multiply.
Let's do some larger problems.
((q^2 - 11q + 24) / (q^2 - 18q + 80)) * ((q^2 - 15q + 50) / (q^2 - 9q + 20))
First, we need to factor. (q^2 - 11q + 24) factors into (q - 8)(q - 3). (q^2 - 18q + 80) factors into (q - 10)(q - 8). (q^2 - 15q + 50) factors into (q - 10)(q - 5). (q^2 - 9q + 20) factors into (q - 5)(q - 4).
So, this is what our new expression is going to look like: ((q - 8)(q - 3) / (q - 10)(q - 8)) * ((q - 10)(q - 5) / (q - 5)(q - 4))
Next, we are going to cancel (what I like to call slash) like terms. We're going to cancel or slash (q - 10) over (q - 10), (q - 8) over (q - 8), and finally (q - 5) over (q - 5).
Now that we have canceled or slashed all of the like terms from the top and bottom, we multiply straight across. Don't multiply anything we slashed because those are now 1's. It turns out, our answer is (q - 3) / (q - 4).
((y^2 - 9) / (2y + 1)) / ((3 - y) / (2y^2 + 7y + 3))
Let's factor. (y - 9) = (y - 3)(y + 3) and (2y^2 + 7y + 3) = (2y + 1)(y + 3). Our next step is to flip the second fraction and change it to multiplication. Our new expression is going to look like this: ((y - 3)(y + 3) / (2y + 1)) * ((2y + 1)(y + 3) / ((3 - y)).
The next step is canceling, or what we've been calling slashing. We can slash (2y + 1) over (2y + 1). In the numerator, we have (y - 3)(y + 3) and (y + 3). In the denominator we have (3 - y). If we multiply (3 - y) by -1, we'll get -1(y - 3). Guess what? We can cancel (y - 3) over (y - 3), but remember to leave the -1!
So, our final answer's going to look like: (y + 3)(y + 3) / -1.
But hold on a second! Let's multiply the top and the bottom by -1. This is going to give us -1(y + 3) (y + 3) / 1. When we FOIL, we're going to end up with an answer of -1(y^2 + 6y + 9) / 1. Well if we distribute the -1, we end up with (-y^2 - 6y - 9)!
((x^2 + x - 2) / (x^2 - 4x - 12)) * ((x^2 - 9x + 8) / (x^2 - 2x + 1)
We begin by factoring. (x^2 + x - 2) factors into (x + 2)(x - 1), (x^2 - 4x - 12) factors into (x - 6)(x + 2), (x^2 - 9x + 8) factors into (x - 8)(x - 1), and x^2 - 2x + 1 factors into (x - 1)(x - 1).
Let's start canceling (or slashing)! We can cancel (x - 1) over (x - 1) and (x + 2) over (x + 2). Once we have canceled, or slashed, all of the terms from the top and bottom, we multiply straight across. That gives us a final answer of (x - 8) / (x - 6).
Multiplication and Division of rational polynomial expressions is easy once you remember the steps!
For multiplication: we factor, cancel or slash, and multiply.
For division: we factor, flip, cancel or slash, and multiply.
By the end of this less you'll easily be able to multiple and divide rational polynomial expressions.
To unlock this lesson you must be a Study.com Member.
Create your account
Already a member? Log In
BackDid you know… We have over 49 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.