Answer
$x^3+12x^2-3x-7$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}