[ ( x+y ) ( x-y ) ] ^ 9 ÷ ( y-x )^ 8 ÷ ( -x-y )^9
= ( x+y )^9 ( x-y ) ^9 ÷ (x-y )^ 8 ÷[- (x+y )^9]
=-[ ( x+y )^9÷( x+y )^9][ ( x-y ) ^9 ÷ (x-y )^ 8]
=-(x-y)
=y-x
[ ( x+y ) ( x-y ) ] ^ 9 ÷ ( y-x )^ 8 ÷ ( -x-y )^9
= ( x+y )^9 ( x-y ) ^9 ÷ (x-y )^ 8 ÷[- (x+y )^9]
=-[ ( x+y )^9÷( x+y )^9][ ( x-y ) ^9 ÷ (x-y )^ 8]
=-(x-y)
=y-x