Intermediate Algebra (12th Edition)

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