Answer
$-7.9x^2+20.3x-7.8$
Work Step by Step
Removing the parenthesis and then combining like terms, the given expression, $
(-4.8x^2+12.5x-7.8)-(3.1x^2-7.8x)
,$ is equivalent to
\begin{array}{l}\require{cancel}
-4.8x^2+12.5x-7.8-3.1x^2+7.8x
\\=
(-4.8x^2-3.1x^2)+(12.5x+7.8x)-7.8
\\=
-7.9x^2+20.3x-7.8
.\end{array}
Let
\begin{array}{l}\require{cancel}Y_1=
(-4.8x^2+12.5x-7.8)-(3.1x^2-7.8x)
,\\Y_2=
-7.9x^2+20.3x-7.8
.\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 $Y_1.$
