## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$a^2-b^2-2bc-c^2$
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}