#### Question

simplify the expression

(x+y-z) (x-y+z) -(x+y+z)(x-y-z)

Question

simplify the expression

(x+y-z) (x-y+z) -(x+y+z)(x-y-z)

Group terms to apply the formula for the difference of squares

(x+y-z) (x-y+z) -(x+y+z)(x-y-z)

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

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

=(y+z)^2-(y-z)^2

=(y+z+y-z)(y+z-y+z)

=4yz