## Intermediate Algebra (12th Edition)

$m^2+2mp+p^2-25$
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the given expression, $[(m+p)-5][(m+p)+5] ,$ is equivalent to \begin{array}{l}\require{cancel} (m+p)^2-(5)^2 \\\\= (m+p)^2-25 .\end{array} Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression above is equivalent to \begin{array}{l}\require{cancel} [(m)^2+2(m)(p)+(p)^2]-25 \\\\= m^2+2mp+p^2-25 .\end{array}