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3u\left(u-8\right)+w\left(u-8\right)
Do the grouping -8w+3u^{2}-24u+uw=\left(3u^{2}-24u\right)+\left(uw-8w\right), and factor out 3u in the first and w in the second group.
\left(u-8\right)\left(3u+w\right)
Factor out common term u-8 by using distributive property.