SOLUTION: I need to Multiply and Solve this Rational Expression. I did it but i don't know if it is right. [x^(3)+y^(3)]/[7y] * [28y^(3)]/[4x+4y] I simplified it by reducing the 7y dividi

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to Multiply and Solve this Rational Expression. I did it but i don't know if it is right. [x^(3)+y^(3)]/[7y] * [28y^(3)]/[4x+4y] I simplified it by reducing the 7y dividi      Log On


   

Question 541642: I need to Multiply and Solve this Rational Expression. I did it but i don't know if it is right. [x^(3)+y^(3)]/[7y] * [28y^(3)]/[4x+4y]
I simplified it by reducing the 7y dividing it into 28y^(3) leaving only 4y^(2) then I pulled the 4 out of the denominator on the second fracion. The 4 in the numerator cancels the 4 in the denominator leaving y^(2) in the numerator and (x+y) in the denominator. Then I did the criss cross thing and subracted (x+y) from the denominator from the [x^(3)+y^(3)] in the numerator in the first part leaving me with [x^(2)+y^(2)] times 4y^(2) which gave me a final answer of x^(2)y+y^(3)
Found 2 solutions by mananth, stanbon:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E%283%29%2By%5E%283%29%29%2F7y%29%2A%28%2828y%5E%283%29%29%2F%284x%2B4y%29%29
%28%28x%5E%283%29%2By%5E%283%29%29%29%2A%28%284y%5E%282%29%29%2F%284%28x%2By%29%29%29
%28x%2By%29%28x%5E2-xy%2By%5E2%29%2A%28%28y%5E%282%29%29%2F%28%28x%2By%29%29%29
cancel off (x+y)
%28x%5E2-xy%2By%5E2%29y%5E2
m.ananth@hotmail.ca






Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
[x^(3)+y^(3)]/[7y] * [28y^(3)]/[4x+4y]
---
The sum of cubes factors as follows:
x^3+y^3 = (x+y)(x^2-xy+y^2)
-----
[(x+y)(x^2-xy+y^2)/(7y)] * [(28y^3/(4(x+y))]
-----
Cancel factors common to numeraor and denominator such as:
(x+y), 7y , 4
--------------------------
= [(x^2-xy+y^2)/1] * [y^2/1]
--------
= (x^2-xy+y^2)*y^2
--------
= x^2y^2-xy^3+y^4
=====================
Cheers,
Stan H.