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a\left(x-y+z\right)+x-y+z
Do the grouping ax-ay+az+x-y+z=\left(ax-ay+az\right)+\left(x-y+z\right), and factor out a in ax-ay+az.
\left(x-y+z\right)\left(a+1\right)
Factor out common term x-y+z by using distributive property.