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4c\left(a+1\right)+b\left(a+1\right)
Do the grouping 4ac+4c+ab+b=\left(4ac+4c\right)+\left(ab+b\right), and factor out 4c in the first and b in the second group.
\left(a+1\right)\left(4c+b\right)
Factor out common term a+1 by using distributive property.