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5y+1+2t\left(5y+1\right)
Do the grouping 5y+1+10ty+2t=\left(5y+1\right)+\left(10ty+2t\right), and factor out 2t in 10ty+2t.
\left(5y+1\right)\left(1+2t\right)
Factor out common term 5y+1 by using distributive property.