$$3a^{2}+27ad^{2}(a+9); a^{3}(a+9)$$
$3\left(a+9\right)\left(9ad^{2}+a+27d^{2}\right)a^{5}$
$$3a\left(a+9d^{2}\left(a+3\right)\right)=3a\left(9ad^{2}+a+27d^{2}\right)$$
$$3\left(a+9\right)\left(9ad^{2}+a+27d^{2}\right)a^{5}$$
$$3a^{7}+27a^{6}+27d^{2}a^{7}+324d^{2}a^{6}+729d^{2}a^{5}$$
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$3a\left(9\left(a+3\right)d^{2}+a\right),\left(a+9\right)a^{5}$
