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4x\left(a+1\right)+a+1
Do the grouping 1+4xa+4x+a=\left(4xa+4x\right)+\left(a+1\right), and factor out 4x in 4xa+4x.
\left(a+1\right)\left(4x+1\right)
Factor out common term a+1 by using distributive property.