## Precalculus (6th Edition) Blitzer

The simplified form of the expression given is $2{{x}^{3}}+{{x}^{2}}-5x+2$.
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 $2{{x}^{3}}+{{x}^{2}}-5x+2$.