问题 填空题

若|p+2|与q2-8q+16互为相反数,分解因式(x2+y2)-(pxy+q)=______.

答案

依题意得|p+2|+(q2-8q+16)=0,即|p+2|+(q-4)2=0,

∴p+2=0,q-4=0,

解得p=-2,q=4,

∴(x2+y2)-(pxy+q),

=(x2+y2)-(-2xy+4),

=x2+y2+2xy-4,

=(x2+2xy+y2)-4,

=(x+y)2-22

=(x+y+2)(x+y-2).

单项选择题
单项选择题