Solve left(v^3-2vright)left(v^-4+v^-2right)

$$\left( { v }^{ 3 } -2v \right) \left( { v }^{ -4 } + { v }^{ -2 } \right)$$

Evaluate

$$v-\frac{1}{v}-\frac{2}{v^{3}}$$

Solution Steps

Use the distributive property to multiply v^{3}-2v by v^{-4}+v^{-2}.

$$v^{3}v^{-4}+v^{3}v^{-2}-2vv^{-4}-2vv^{-2}$$

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$v^{-1}+v^{3}v^{-2}-2vv^{-4}-2vv^{-2}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$v^{-1}+v^{1}-2vv^{-4}-2vv^{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$v^{-1}+v^{1}-2v^{-3}-2vv^{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$v^{-1}+v^{1}-2v^{-3}-2v^{-1}$$

Calculate v to the power of 1 and get v.

$$v^{-1}+v-2v^{-3}-2v^{-1}$$

Combine v^{-1} and -2v^{-1} to get -v^{-1}.

$$-v^{-1}+v-2v^{-3}$$

Expand

$$v-\frac{1}{v}-\frac{2}{v^{3}}$$

Solution Steps

Use the distributive property to multiply v^{3}-2v by v^{-4}+v^{-2}.

$$v^{3}v^{-4}+v^{3}v^{-2}-2vv^{-4}-2vv^{-2}$$

To multiply powers of the same base, add their exponents. Add 3 and -4 to get -1.

$$v^{-1}+v^{3}v^{-2}-2vv^{-4}-2vv^{-2}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$v^{-1}+v^{1}-2vv^{-4}-2vv^{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$v^{-1}+v^{1}-2v^{-3}-2vv^{-2}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$v^{-1}+v^{1}-2v^{-3}-2v^{-1}$$

Calculate v to the power of 1 and get v.

$$v^{-1}+v-2v^{-3}-2v^{-1}$$

Combine v^{-1} and -2v^{-1} to get -v^{-1}.

$$-v^{-1}+v-2v^{-3}$$