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### Course: Algebra (all content)>Unit 10

Lesson 11: Factoring monomials

# Worked example: finding missing monomial side in area model

Learn how to find the length of a rectangle using algebraic expressions, as Sal finds the length of a rectangle whose area is 42xy^3 and whose height is 14xy. Dive into dividing coefficients and variables to solve for length and uncover how dividing powers of 'y' can simplify your equation.

## Want to join the conversation?

• Who came up with this theory?
• No one knows but the theory is called Discriminant
• When we divide x by x, don't we get x to the zero power?
• Not exactly. x/x = 1 because that is just a fraction rule. 8/8 = 1, 8532/8532 = 1 and so on
• What if you distributed L?
Why do we not? Is it because it's a monomial?
• Correct. There isn't anywhere to distribute it to because L and 14xy are both monomials:
L(14xy) distributed would just be L14xy . Which doesn't actually change anything - it just makes the equation look a little more sloppy.
• How did we get the 3y^2 at the end? I got 3xy^2 as my answer. Did Mr.Sal get the 3y^2 because when he divided 42x and 14x, did the x's cancel out?
• yep, variables can cencel out when dividing. x/x = 1, (x^2)/x = x and x/(x^2) = 1/x. then you can just plug in other exponents to make it work.

It might even be easier to think of it with numbers. (2^5) / (2^3) = 2^2
• How do you find the area of a missing side of a shape? and how do you find the missing side of a triangle when given the area?
• We divide the are from the given length (regarding the formula of area for a particular shape)
• What if you distributed L?
Why do we not? Is it because it's a monomial?
(1 vote)
• 'Distribute' means 'apply the distributive property', which is that a(b+c)=ab+ac. It's a property of multiplication and addition.

There is no addition in this example, so the distributive property doesn't apply.
(1 vote)
• Do we need to specify that 14xy is not equal to 0 ?
(1 vote)
• what if my area is 12y^2+21y^5 and im trying to find the width and length using factroring?
(1 vote)
• You can extract 3y^2 from both sides.
12y^2+21y^5
= 3y^2(7y^3 + 4)
From there you factor it out and find out your y values.
I hope this helped!
(1 vote)

## Video transcript

- [Voiceover] So we have a rectangle right over here. Let's say that we know that its area is 42x times y to the third. So that is the area of the rectangle. And we also know that the height right over here is 14xy and what we want to do in this video is figure out what the length is going to be. And as you can imagine, it's going to be in algebraic terms. So I encourage you to pause the video and figure out what is the length going to be if this height is 14xy and the area is 42xy to the third. Well, how do you figure out area? You take your length, and I'll just use L for length. I'll put L in parentheses. So you take your length and you multiply it times your height. So let's multiply it times 14xy and that's going to give you your area. So that's going to give us our area of 42xy to the third power. So how do we solve for our length? Well, we can just divide both sides by 14xy. So let's do that. So, let's divide the left-hand side and the right-hand side by 14xy, 14xy. Now on the left-hand side, I'm multiplying by 14xy and dividing by 14xy, that's the same thing as just multiplying or dividing by one so that cancels out. So I'm just left with L or our length which is the whole point of dividing both sides by 14xy. And on the right-hand side, I can look at the coefficients first. I could say 42 divided by 14, and that's going to be three. Three, and then I could say well, x divided by x that's just going to be one, and then I have y to the third divided by y. y to the third divided by y, that is going to be y to the third divided by y is going to be y-squared. And then we're done. Our length is three y-squared. So our length is equal to three y-squared.