Answer: [tex]-p^2-(q+r)^2[/tex]
Work Shown:
I'm assuming your teacher wants you to factor as much as possible.
[tex]-p^2-q^2-r^2-2qr\\\\-p^2-q^2-2qr-r^2\\\\-p^2-(q^2+2qr+r^2)\\\\-p^2-(q+r)^2\\\\[/tex]
In the last step, I used the rule that [tex](a+b)^2 = a^2+2ab+b^2[/tex]
We cannot factor any further. If the first term was [tex]p^2[/tex] instead of [tex]-p^2[/tex], then we could use the difference of squares factoring rule.
