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2\left(2x^{2}+x+4yx+2y\right)
Factor out 2.
x\left(2x+1\right)+2y\left(2x+1\right)
Consider 2x^{2}+x+4yx+2y. Do the grouping 2x^{2}+x+4yx+2y=\left(2x^{2}+x\right)+\left(4yx+2y\right), and factor out x in the first and 2y in the second group.
\left(2x+1\right)\left(x+2y\right)
Factor out common term 2x+1 by using distributive property.
2\left(2x+1\right)\left(x+2y\right)
Rewrite the complete factored expression.