若|P+2|与q²-8q+16互为相反数,分解因式（X²+y²）-(pxy+q)=?

若|P+2|与q²-8q+16互为相反数,分解因式（X²+y²）-(pxy+q)=?

|P+2|>=0
q²-8q+16=(q-4)^2>=0
|P+2|与q²-8q+16互为相反数
则P+2=0 P=-2
(q-4)^2=0 q=4
（X²+y²）-(pxy+q)
=x^2+y^2+2xy-4
=(x-y)^2-2^2
=(x-y-2)(x-y+2)