## College Algebra (6th Edition)

$6x^{n}-13$
$(x^{n}+2)(x^{n}-2)-(x^{n}-3)^{2}$ 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 $= x^{2n} - x^{2n} + 6x^{n} - 4 -9$ $= 6x^{n} - 13$