Answer
$6x^{n}-13$
Work Step by Step
$(x^{n}+2)(x^{n}-2)-(x^{n}-3)^{2}$
To find the product of the sum and difference of two terms, use the formula,
$(a+b)(a-b)=a^{2}-b^{2}$
and the square of the binomial can be found using the formula,
$(a-b)^{2}=a^{2}-2ab+b^{2}$
$(x^{n}+2)(x^{n}-2)-(x^{n}-3)^{2}$
$= (x^{ n})^{2}-2^{2} - [ (x^{ n})^{2} - 2(x^{n})(3)+3^{2} ]$
$= x^{2n} - 4 - [x^{2n}- 6x^{n}+9]$
$= x^{2n} - 4 - x^{2n} + 6x^{n} -9 $
Combine like terms
$= x^{2n} - x^{2n} + 6x^{n} - 4 -9 $
$= 6x^{n} - 13$
