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a^{2}\left(b^{2}+d\right)+c\left(b^{2}+d\right)
Do the grouping a^{2}b^{2}+cd+b^{2}c+a^{2}d=\left(a^{2}b^{2}+a^{2}d\right)+\left(b^{2}c+cd\right), and factor out a^{2} in the first and c in the second group.
\left(b^{2}+d\right)\left(a^{2}+c\right)
Factor out common term b^{2}+d by using distributive property.