Answer
$(a+1)^2(a+3)(a-1)$
Work Step by Step
$Factor$ $the$ $expression$ $completely:$
$(a^2+2a)^2 - 2(a^2+2a) - 3$
We can identify the expression is in trinomial form, so we can factor it to two binomials
$(a^2+2a)^2 - 2(a^2+2a) - 3$ = $((a^2+2a)+1)((a^2+2a)-3)$
Simplify the binomials
$= (a^2+2a+1)(a^2+2a-3)$
Since we simplified, the two binomials turned into two trinomials, so we factor those two trinomials to two binomials each
$(a^2+2a+1)$ = $(a+1)(a+1)$ = $(a+1)^2$
$(a^2+2a-3)$ = $(a+3)(a-1)$
$= (a+1)^2(a+3)(a-1)$
