SOLUTION: Hello! I need help with this question please! I do not understand. There are two square workout mats at a gym. a. Let x represent the length of the larger mat, and let y rep

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello! I need help with this question please! I do not understand. There are two square workout mats at a gym. a. Let x represent the length of the larger mat, and let y rep      Log On


   

Question 1065139: Hello! I need help with this question please! I do not understand.
There are two square workout mats at a gym.
a. Let x represent the length of the larger mat, and let y represent the length of the smaller mat. Write a binomial that represents how much more area the larger mat has than the smaller mat.
b. factor the binomial for the difference in the mat areas. Interpret what the factors could mean in this context.
c. One mat has 4 times the area of the other mat. Use this to rewrite the binomial from part a using only the variable y.
Thank you in advance!!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length of the side of the larger square workout mat
y= length of the side of the smaller square workout mat

a. We calculate the surface area of each mat
x%2Ax=x%5E2= surface area of the larger square workout mat
y%2Ay=y%5E2= surface area of the smaller square workout mat
highlight%28x%5E2-y%5E2%29= binomial that represents how much more area the larger mat has than the smaller mat.

b. highlight%28x%5E2-y%5E2=%28x%2By%29%2A%28x-y%29%29 is the factoring
%28x%2By%29 means the sum of the side lengths of the two mats
%28x-y%29 means the difference of the side lengths of the two mats
Here is how to visualize those factors with the mats placed side by side.


c. x%5E2=4y%5E2 says that the larger mat has 4 times the area of the other mat.
Substituting 4y%5E2 for x%5E2 in the binomial expression x%5E2-y%5E2 ,
we get 4y%5E2-y%5E2=highlight%283y%5E2%29 .