Answer
$3(a+6b)(a+3b)$
Work Step by Step
$ 3a^{2}+27ab+54b^{2}\qquad$... factor out the common term, $3$
$=3(a^{2}+9ab+18b^{2})$
... Searching for two factors of $ac=18$ whose sum is $b=9,$
we find$\qquad 6$ and $3.$
Rewrite the middle term and factor in pairs:
$=3(a^{2}+6ab+3ab+18b^{2})=$
$=3[a(a+6b)+3b(a+6b)]$
= $3(a+6b)(a+3b)$
