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\left(p+r-o\right)\left(p+r+o\right)
Rewrite p^{2}+2pr+r^{2}-o^{2} as \left(p+r\right)^{2}-o^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).