Chapter 5 - Section 5.3 - Special Products - Exercise Set - Page 367: 41

$1-y^8$

Using $(a+b)(a-b)=a^2-b^2$ or the special product of the sum and difference of like terms, the product of the given expression, $ (1-y^4)(1+y^4) ,$ is \begin{array}{l}\require{cancel} 1(1)-y^4(y^4) \\\\= 1-y^8 .\end{array}