## Intermediate Algebra (12th Edition)

$x^3+12x^2-3x-7$
$\bf{\text{Solution Outline:}}$ Use the Distributive Property and then combine like terms to simplify the given expression, $(3x^3+4x^2-7)-(2x^3-8x^2+3x) .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} (3x^3+4x^2-7)-1(2x^3-8x^2+3x) \\\\= (3x^3+4x^2-7)-1(2x^3)-1(-8x^2)-1(3x) \\\\= 3x^3+4x^2-7-2x^3+8x^2-3x .\end{array} Combining like terms results to \begin{array}{l}\require{cancel} (3x^3-2x^3)+(4x^2+8x^2)-3x-7 \\\\ x^3+12x^2-3x-7 .\end{array}