## Intermediate Algebra (12th Edition)

$4a^2+4ab+b^2-9$
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the given expression, $[(2a+b)-3][(2a+b)+3] ,$ is equivalent to \begin{array}{l}\require{cancel} (2a+b)^2-(3)^2 \\\\= (2a+b)^2-9 .\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} [(2a)^2+2(2a)(b)+(b)^2]-9 \\\\= 4a^2+4ab+b^2-9 .\end{array}