Answer
$x^3-4x^2+7x-8$
Work Step by Step
Removing the parenthesis and then combining like terms, the given expression, $
(2x^2+7x+6)+(x^3-6x^2-14)
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x^2+7x+6+x^3-6x^2-14
\\=
x^3+(2x^2-6x^2)+7x+(6-14)
\\=
x^3-4x^2+7x-8
.\end{array}
Let
\begin{array}{l}\require{cancel}Y_1=
(2x^2+7x+6)+(x^3-6x^2-14)
,\\Y_2=
x^3-4x^2+7x-8
.\end{array}
Using a graphing calculator, the graphs of $Y_1$ (dotted graph) and $Y_2$ (solid graph) are shown below. Since the graphs overlap, then $Y_2$ is the correct simplification of $Y_1.$
