1. Factor p^2-2p+1-q^2-2qr-r^2 as the product of two polynomials of degree 1.

1. Factor p^2-2p+1-q^2-2qr-r^2 as the product of two polynomials of degree 1.

p^2-2p+1-q^2-2qr-r^2 a  =

(p - 1)^2 - (q  + r)^2  =

[ (p -1)  + (q + r) ] [ ( p - 1) - (q + r)]  =

[ p + q + r - 1]  [ p - q - r - 1 ]

2. Factor 4x^2y^2-(x^2+y^2-z^2)^2 as the product of four polynomials of degree 1. 

4x^2y^2-(x^2+y^2-z^2)^2  =

[2xy + ( x^2 + y^2 - z^2) ]  [  2xy - (x^2 + y^2 - z^2)]  =

[[ x^2 + 2xy + y^2] - z^2 ] [ 2xy - x^2 -y^2 + z^2 ]  =

[ (x + y)^2 - z^2]  (-1)[ x^2 - 2xy + y^2 - z^2]  =

[ (x + y)^2 - z^2] (-1) [ ( x - y)^2 - z^2]  =

[ (x + y)^2 - z^2] [ z^2 - (x - y)^2]  =

[(x + y) + z ] [ (x + y - z] [ z + (x - y)] [ z - (x - y)]  =

[ x + y + z ] [ x + y - z ] [ x - y + z] [ -x + y + z ]