Answer
$88$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{v \to 2} \left( {{v^2} + 2v} \right)\left( {2{v^3} - 5} \right) \cr
& {\text{Suppose that }}c{\text{ is a constant and the limits }} \cr
& {\text{ }}\mathop {\lim }\limits_{x \to a} f\left( x \right){\text{ and }}\mathop {\lim }\limits_{x \to a} g\left( x \right) \cr
& \cr
& {\text{Use the Product Law}} \cr
& \mathop {\lim }\limits_{x \to a} \left[ {f\left( x \right)g\left( x \right)} \right] = \mathop {\lim }\limits_{x \to a} f\left( x \right) \cdot \mathop {\lim }\limits_{x \to a} g\left( x \right) \cr
& = \left[ {\mathop {\lim }\limits_{v \to 2} \left( {{v^2} + 2v} \right)} \right]\left[ {\mathop {\lim }\limits_{v \to 2} \left( {2{v^3} - 5} \right)} \right] \cr
& \cr
& {\text{Use the Sum and Difference Laws }}\left( {{\text{see page 95}}} \right) \cr
& \mathop {\lim }\limits_{x \to a} \left[ {f\left( x \right) + g\left( x \right)} \right] = \mathop {\lim }\limits_{x \to a} f\left( x \right) + \mathop {\lim }\limits_{x \to a} g\left( x \right) \cr
& = \left[ {\mathop {\lim }\limits_{v \to 2} \left( {{v^2}} \right) + \mathop {\lim }\limits_{v \to 2} \left( {2v} \right)} \right]\left[ {\mathop {\lim }\limits_{v \to 2} \left( {2{v^3}} \right) - \mathop {\lim }\limits_{v \to 2} \left( 5 \right)} \right] \cr
& \cr
& {\text{Use the Constant Multiple Law }}\left( {{\text{see page 95}}} \right) \cr
& \mathop {\lim }\limits_{x \to a} \left[ {cf\left( x \right)} \right] = c\mathop {\lim }\limits_{x \to a} f\left( x \right) \cr
& = \left[ {\mathop {\lim }\limits_{v \to 2} \left( {{v^2}} \right) + 2\mathop {\lim }\limits_{v \to 2} \left( v \right)} \right]\left[ {\mathop {2\lim }\limits_{v \to 2} \left( {{v^3}} \right) - \mathop {\lim }\limits_{v \to 2} \left( 5 \right)} \right] \cr
& \cr
& {\text{Use The power Law }}\mathop {\lim }\limits_{x \to a} {x^n} = {a^n}{\text{, }}n{\text{ is a positive integer }} \cr
& {\text{and the laws }}\mathop {\lim }\limits_{x \to a} x = a,{\text{ }}\mathop {\lim }\limits_{x \to a} c = c,{\text{ then}} \cr
& = \left[ {{{\left( 2 \right)}^2} + 2\left( 2 \right)} \right]\left[ {2{{\left( 2 \right)}^3} - \left( 5 \right)} \right] \cr
& {\text{Simplifying}} \cr
& = \left( {4 + 4} \right)\left( {16 - 5} \right) \cr
& = 88 \cr} $$
