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5x\left(2x+1\right)+y\left(2x+1\right)
Do the grouping 10x^{2}+5x+2xy+y=\left(10x^{2}+5x\right)+\left(2xy+y\right), and factor out 5x in the first and y in the second group.
\left(2x+1\right)\left(5x+y\right)
Factor out common term 2x+1 by using distributive property.