SOLUTION: I was trying to work this problem and ended up with a lock up ( I call this )when you have a bunch of letters and numbers that keep repeating themselves. I am sure that I am doing

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I was trying to work this problem and ended up with a lock up ( I call this )when you have a bunch of letters and numbers that keep repeating themselves. I am sure that I am doing       Log On


   

Question 70035This question is from textbook Beginning Algebra
: I was trying to work this problem and ended up with a lock up ( I call this )when you have a bunch of letters and numbers that keep repeating themselves. I am sure that I am doing this incorrectly. Please Help.
7x^5 y^5 - 21x^4 y^4 + 14x^3 y^3/ 7x^3 y^3
Thanks. This question is from textbook Beginning Algebra

Found 2 solutions by funmath, bucky:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!

7x^5 y^5 - 21x^4 y^4 + 14x^3 y^3/ 7x^3 y^3
If this is what you mean:
%287x%5E5%2Ay%5E5-21x%5E4y%5E4%2B14x%5E3y%5E3%29%2F%287x%5E3y%5E3%29
you can factor and cancel.
7x%5E3y%5E3%28x%5E2y%5E2-3xy%2B2%29%2F%287x%5E3y%5E3%29
cross%287x%5E3y%5E3%29%28x%5E2y%5E2-3xy%2B2%29%2Fcross%287x%5E3y%5E3%29
highlight%28x%5E2y%5E2-3xy%2B2%29
Or if you prefer, when the bottom is a monomial you can separate and cancel:


1x%5E2y%5E2-3x%5E1y%5E1%2B2x%5E0y%5E0
x%5E2y%5E2-3xy%2B2%281%29%281%29
highlight%28x%5E2y%5E2-3xy%2B2%29
Both are valid ways of simplifying this expression.
Happy Calculating!!!!

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!

.
Notice that 7 can be factored from each of the terms in the numerator so that the problem
becomes:
.
7%2A%28x%5E5%2Ay%5E5+-3%2Ax%5E4%2Ay%5E4+%2B+2%2Ax%5E3%2Ay%5E3%29%2F%287%2Ax%5E3%2Ay%5E3%29
.
In this form it is easier to recognize that the multiplier 7 in the numerator cancels
with the multiplier 7 in the denominator to reduce the problem to:
.
%28x%5E5%2Ay%5E5+-3%2Ax%5E4%2Ay%5E4+%2B+2%2Ax%5E3%2Ay%5E3%29%2F%28x%5E3%2Ay%5E3%29
.
Similarly, you can next factor an x%5E3 from every term in the numerator to get:
.
x%5E3%2A%28x%5E2%2Ay%5E5+-3%2Ax%2Ay%5E4+%2B+2%2Ay%5E3%29%2F%28x%5E3%2Ay%5E3%29
.
Then notice that this x%5E3 multiplier in the numerator cancels with the x%5E3
multiplier in the denominator. This reduces the problem to:
.
%28x%5E2%2Ay%5E5+-3%2Ax%2Ay%5E4+%2B+2%2Ay%5E3%29%2F%28y%5E3%29
.
Finally, you can factor a y%5E3 from every term in the numerator to get:
.
y%5E3%2A%28x%5E2%2Ay%5E2+-3%2Ax%2Ay+%2B+2%29%2F%28y%5E3%29
.
And recognize that the y%5E3 multiplier of the numerator cancels with the y%5E3
in the denominator to leave you with just:
.
%28x%5E2%2Ay%5E2+-3%2Ax%2Ay+%2B+2%29%29
.
This might be the answer you were looking for, but notice also that this can be factored
into:
.
%28xy+-+2%29%2A%28xy+-+1%29
.
and maybe this is the answer form you were looking for.
Hope this helps you to see a form for dividing polynomials that might be useful.