Answer
$\text{(a) } 2x^2-3x+3$
$\text{(b) } 6x^3-4x^2+3x-2$
$\text{(c) } 4xh+2h^2$
Work Step by Step
Given $f(x)=2x^2+1$ and $g(x)=3x-2$, we can find:
$\text{(a) }(f-g)(x)=f(x)-g(x)=(2x^2+1)-(3x-2)=2x^2-3x+3$
$\text{(b) }(f\cdot g)(x)=f(x)\cdot g(x)=(2x^2+1)(3x-2)=6x^3-4x^2+3x-2$
$\text{(c) }\\
\begin{align*}f(x+h)-f(x)&=2(x+h)^2+1-(2x^2+1)\\
&=2(x^2+2hx+h^2)+1-2x2-1\\
&=2x^2+4hx+2h^2+1-2x^2-1\\
&=4xh+2h^2
\end{align*}$
