Question 423350
area is equal to:


9x^2 - 6xy + y^2


this would be factored as:


(3x-y) * (3x-y)


multiply these factors out and you get 9x^2 - 6xy + y^2 which is the original equation.


when x = 12 and y = 6, this becomes:


(36-6) * (36-6) = 30*30 = 900 square units.


plug those values into the original equation:


9x^2 - 6xy + y^2 becomes 9*12^2 - 6*12*6 + 6^2 becomes 9*144 - 12*36 + 36 becomes 1296 - 432 + 36 becomes 900.


you get the same answer, as you should.


the rectangle field is really a square.


you get this from the fact that (3x-y) * (3x-y) = area of the field.


since the area of a rectangle is length * width, then:


the length is 3x-y and the width is 3x-y.


when x = 12 and y = 6, this comes out to a length of 30 and a width of 30.