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2x\left(ay^{2}+5\right)+3\left(ay^{2}+5\right)
Do the grouping 2axy^{2}+10x+3ay^{2}+15=\left(2axy^{2}+10x\right)+\left(3ay^{2}+15\right), and factor out 2x in the first and 3 in the second group.
\left(ay^{2}+5\right)\left(2x+3\right)
Factor out common term ay^{2}+5 by using distributive property.