Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 11

$(x+4)^2$

The 2 numbers whose product is $ac= 1(16)=16 $ and whose sum is $b= 8 $ are $\left\{ 4,4 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $ x^2+8x+16 ,$ then \begin{array}{l}\require{cancel} x^2+4x+4x+16 \\\\= (x^2+4x)+(4x+16) \\\\= x(x+4)+4(x+4) \\\\= (x+4)(x+4) \\\\= (x+4)^2 .\end{array}