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

$-2x^3-6x^2-x-3$
The given expression, $(4x-5x-3)(1+2x^2) ,$ is equivalent to \begin{array}{l}\require{cancel} (-x-3)(1+2x^2) .\end{array} Using $(a+b)(c+d)=ac+ad+bc+bd$ or the product of 2 binomials, the expression above is equivalent to \begin{array}{l}\require{cancel} -x(1)-x(2x^2)-3(1)-3(2x^2) \\\\= -x-2x^3-3-6x^2 \\\\= -2x^3-6x^2-x-3 .\end{array}