Answer
$ (a+1)(a-1)(a+2)(a-2)$
Work Step by Step
$Factor$ $the$ $expression$ $completely:$
$(a^2+1)^2 - 7(a^2+1) + 10$
We can identify that the expression is in trinomial form, so we can factor it into two binomials
$(a^2+1)^2 - 7(a^2+1) + 10$ = $((a^2+1)-2)((a^2+1)-5)$
Simplify the binomials
$= (a^2+1-2)(a^2+1-5)$
$= (a^2-1)(a^2-4)$
Use the Difference of Squares Formula for both binomials
Difference of Squares Formula: $(A^2-B^2) = (A-B)(A+B)$
$(a^2-1) = (a+1)(a-1)$
$(a^2-4) = (a+2)(a-2)$
$= (a+1)(a-1)(a+2)(a-2)$
