SOLUTION: 25y^4-20t^6y^4/5x^4y^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 25y^4-20t^6y^4/5x^4y^2      Log On


   

Question 280343: 25y^4-20t^6y^4/5x^4y^2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I assume the expression is
%2825y%5E4-20t%5E6y%5E4%29%2F5x%5E4y%5E2
(In the future, please enclose multi-term numerators or denominators in parentheses.)

This is an expression and all you can do with an expression is simplify it. With a fraction, that means reducing it. To reduce a fraction you cancel factors which are common to the numerator and denominator, if any. So we need to see what the factors are by factoring the numerator and denominator. The denominator is a single term so it is already a product. But the numerator needs to be factored. The Greatest Common Factor (GCF) in the numerator is 5y%5E4:
%285y%5E4%285-4t%5E6%29%29%2F5x%5E4y%5E2
The numerator will not factor any further. Even so we have some common factors to cancel: 5 and y%5E2.
%285y%5E2y%5E2%285-4t%5E6%29%29%2F5x%5E4y%5E2
%28cross%285%29cross%28y%5E2%29y%5E2%285-4t%5E6%29%29%2Fcross%285%29x%5E4cross%28y%5E2%29
leaving:
%28y%5E2%285-4t%5E6%29%29%2Fx%5E4
Multiplying out the numerator we get:
%285y%5E2-4t%5E6y%5E2%29%2Fx%5E4