# Chapter 5 - Sections 5.1-5.7 - Integrated Review - Operations on Polynomials and Factoring Strategies - Page 313: 21

$(2x+9)^2$

#### Work Step by Step

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

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