Answer
$x^2+2xy+y^2-4z^2$
Work Step by Step
Grouping the first 2 terms of each trinomial factor, the given expression, $
(x+y+2z)(x+y-2z)
,$ is equivalent to
\begin{array}{l}\require{cancel}
[(x+y)+2z][(x+y)-2z]
.\end{array}
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the expression above simplifies to
\begin{array}{l}\require{cancel}
(x+y)^2-(2z)^2
\\\\=
(x+y)^2-4z^2
.\end{array}
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression above simplifies to
\begin{array}{l}\require{cancel}
(x)^2+2(x)(y)+(y)^2-4z^2
\\\\=
x^2+2xy+y^2-4z^2
.\end{array}