Question

Factor the following polynomial completely. - x2y2 + x4 + 9 y2 - 9 x2 ( x - 3)( x - 3)( x + y )( x - y ) ( x + 3)( x + 3)( x + y )( x - y ) ( x + 3)( x - 3)( x + y )( x - y )

Answer 1

Answer:

  ( x + 3)( x - 3)( x + y )( x - y )

Step-by-step explanation:

You can group the terms in pairs and factor each pair:

  -x^2y^2 + x^4 + 9y^2 - 9x^2 = x^2(-y^2+x^2) -9(-y^2+x^2)

  = (x^2 -9)(x^2 -y^2)

Each of these factors is the difference of squares, so can be factored as such:

  = (x +3)(x -3)(x +y)(x -y)