Answer
The simplified form of the expression given is $2{{x}^{3}}+{{x}^{2}}-5x+2$.
Work Step by Step
Consider the given expression $\left( 2x-1 \right)\left( {{x}^{2}}+x-2 \right)$.
Simplify the given product expression using the distributive property as below:
$\begin{align}
& \left( 2x-1 \right)\left( {{x}^{2}}+x-2 \right)=2x\left( {{x}^{2}}+x-2 \right)-1\left( {{x}^{2}}+x-2 \right) \\
& =2{{x}^{3}}+2{{x}^{2}}-4x-{{x}^{2}}-x+2 \\
& =2{{x}^{3}}+{{x}^{2}}-5x+2
\end{align}$
Hence, the simplified form is $2{{x}^{3}}+{{x}^{2}}-5x+2$.
