Chapter 5 - Polynomials and Factoring - 5.4 Factoring Perfect-Square Trinomials and Differences of Squares - 5.4 Exercise Set - Page 333: 92

$(a^2+9b^2)(a+3b)(a-3b)$

Using $x^2-y^2=(x+y)(x-y)$ or the factoring of the difference of 2 squares, then the factored form of the given expression, $ a^4-81b^4 ,$ is \begin{array}{l} (a^2+9b^2)(a^2-9b^2) \\\\= (a^2+9b^2)(a+3b)(a-3b) \end{array}