Answer
$a^2+2ab+b^2-c^2$
Work Step by Step
Grouping the first 2 terms of each trinomial factor, the given expression, $
(a+b-c)(a+b+c)
,$ is equivalent to
\begin{array}{l}\require{cancel}
[(a+b)-c][(a+b)+c]
.\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}
(a+b)^2-(c)^2
\\\\=
(a+b)^2-c^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}
(a)^2+2(a)(b)+(b)^2-c^2
\\\\=
a^2+2ab+b^2-c^2
.\end{array}