Answer
$a^2-b^2-2bc-c^2$
Work Step by Step
Using grouping symbols, 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)^2-(b+c)^2
\\\\=
a^2-(b+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-[(b)^2+2(b)(c)+(c)^2]
\\\\=
a^2-[b^2+2bc+c^2]
\\\\=
a^2-b^2-2bc-c^2
.\end{array}
