Chapter 5 - Sections 5.1-5.7 - Integrated Review - Operations on Polynomials and Factoring Strategies - Page 313: 53

$(2b-9)^2$

The two numbers whose product is $ 81(4)=324 $ and whose sum is $ -36 $ are $\{ -18,-18 \}$. Using these numbers to decompose the middle term of the trinomial results to \begin{array}{l} 4b^2-36b+81 \\= 4b^2-18b-18b+81 \\= (4b^2-18b)-(18b-81) \\= 2b(2b-9)-9(2b-9) \\= (2b-9)(2b-9) \\= (2b-9)^2 .\end{array}