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gp\left(p-r\right)-2r\left(p-r\right)
Do the grouping p^{2}g-pgr-2pr+2r^{2}=\left(p^{2}g-pgr\right)+\left(-2pr+2r^{2}\right), and factor out gp in the first and -2r in the second group.
\left(p-r\right)\left(gp-2r\right)
Factor out common term p-r by using distributive property.