## Intermediate Algebra (12th Edition)

$2x^3+22x^2+56x$
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the product of the binomials in the given expression, $2x(x+4)(x+7) ,$ is \begin{array}{l}\require{cancel} 2x[x(x)+x(7)+4(x)+4(7)] \\\\= 2x[x^2+7x+4x+28] \\\\= 2x[x^2+11x+28] .\end{array} Using $a(b+c)=ab+ac$ or the Distributive Property, the product of the expression above is \begin{array}{l}\require{cancel} 2x(x^2)+2x(11x)+2x(28) \\\\= 2x^3+22x^2+56x .\end{array}