Answer
$6y^n-13$.
Work Step by Step
The given expression is
$=(y^n+2)(y^n-2)-(y^n-3)^2$
Use Algebra identity.
$(a+b)(a-b)=a^2-b^2$
Plug $a=y^n$ and $b=2$.
$(y^n+2)(y^n-2)=(y^n)^{2}-(2)^2$
$(y^n+2)(y^n-2)=y^{2n}-4$
Now use Algebra identity.
$(a-b)^2=a^2-2ab+b^2$
Plug $a=y^n$ and $b=3$
$(y^n-3)^2=(y^n)^2-2(y^n)(3)+(3)^2$
$(y^n-3)^2=y^{2n}-6y^n+9$
The given expression will be.
$=y^{2n}-4-(y^{2n}-6y^n+9)$
Simplify.
$=y^{2n}-4-y^{2n}+6y^n-9$
Add like terms.
$=6y^n-13$.
