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x\left(2a^{2}+b\right)-\left(2a^{2}+b\right)
Do the grouping 2a^{2}x+bx-2a^{2}-b=\left(2a^{2}x+bx\right)+\left(-2a^{2}-b\right), and factor out x in the first and -1 in the second group.
\left(2a^{2}+b\right)\left(x-1\right)
Factor out common term 2a^{2}+b by using distributive property.