SOLUTION: Without expanding. Find the value of the determinant |x y 1 | |x^2 y^2 x+y | |x^3 y^3 x^2+xy+y2 |

It does not change the value of a determinant to
multiply a row by a constant and add it
to another row. 

 

Multiply the 2nd row by -x and add it to the 3rd row:

 

Multiply the 1st row by -x and add it to the 2nd row:



Multiply the 2nd row by -y and add it to the 3rd row:

 

The bottom row has all 0's, so the value of the 
determinant is 0.

Edwin