Question 502904
(7x^(2)y+21xy^(2)-28y^(3))/(36x^(3)y-27x^(2)y^(2)-9xy^(3))

Factor out the GCF of 7y from each term in the polynomial.
(7y(x^(2))+7y(3xy)+7y(-4y^(2)))/(36x^(3)y-27x^(2)y^(2)-9xy^(3))

Factor out the GCF of 7y from 7x^(2)y+21xy^(2)-28y^(3).
(7y(x^(2)+3xy-4y^(2)))/(36x^(3)y-27x^(2)y^(2)-9xy^(3))

For a polynomial of the form x^(2)+bx+c, find two factors of c (-4) that add up to b (3).  In this problem 4*-1=-4 and 4-1=3, so insert 4 as the right hand term of one factor and -1 as the right-hand term of the other factor.
(7y(x+4y)(x-y))/(36x^(3)y-27x^(2)y^(2)-9xy^(3))

Factor out the GCF of 9xy from each term in the polynomial.
(7y(x+4y)(x-y))/(9xy(4x^(2))+9xy(-3xy)+9xy(-y^(2)))

Factor out the GCF of 9xy from 36x^(3)y-27x^(2)y^(2)-9xy^(3).
(7y(x+4y)(x-y))/(9xy(4x^(2)-3xy-y^(2)))

Find the factors such that the product of the factors is the trinomial 4x^(2)-3xy-y^(2).  This can be done by trial and error and checked using the FOIL method of simplifying polynomials.
(7y(x+4y)(x-y))/(9xy(4x+1y)(x-1y))

Reduce the expression (7y(x+4y)(x-y))/(9xy(4x+y)(x-y)) by removing a factor of y from the numerator and denominator.
(7(x+4y)(x-y))/(9x(4x+y)(x-y))

Reduce the expression by canceling out the common factor of (x-y) from the numerator and denominator.
(7(x+4y)<X>(x-y)<x>)/(9x(4x+y)<X>(x-y)<x>)

Reduce the expression by canceling out the common factor of (x-y) from the numerator and denominator.
(7(x+4y))/(9x(4x+y))  лл Answer.