Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set - Page 436: 41

$(a-3b)(a-15b)$

The given expression, $ a^2-18ab+45b^2 ,$ has $c= 45 $ and $b= -18 .$ The possible factors of $c$ are $ \{ 1,45 \} ,\{ 3,15 \} ,\{ 5,9 \} ,\{ -1,-45 \} ,\{ -3,-15 \} ,\{ -5,-9 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -3,-15 \}.$ Hence, the factored form is \begin{array}{l}\require{cancel} (a-3b)(a-15b) .\end{array}