Solve H(u)=(u^-1+2u^-3)(u^4-3u^3)

$$H ( u ) = ( u ^ { - 1 } + 2 u ^ { - 3 } ) ( u ^ { 4 } - 3 u ^ { 3 } )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply u^{-1}+2u^{-3} by u^{4}-3u^{3}.

$$u^{-1}u^{4}-3u^{-1}u^{3}+2u^{-3}u^{4}-6$$

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

$$u^{3}-3u^{-1}u^{3}+2u^{-3}u^{4}-6$$

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

$$u^{3}-3u^{2}+2u^{-3}u^{4}-6$$

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

$$u^{3}-3u^{2}+2u^{1}-6$$

Calculate u to the power of 1 and get u.

$$u^{3}-3u^{2}+2u-6$$

Expand

$$u^{3}-3u^{2}+2u-6$$

Solution Steps

Use the distributive property to multiply u^{-1}+2u^{-3} by u^{4}-3u^{3}.

$$u^{-1}u^{4}-3u^{-1}u^{3}+2u^{-3}u^{4}-6$$

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

$$u^{3}-3u^{-1}u^{3}+2u^{-3}u^{4}-6$$

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

$$u^{3}-3u^{2}+2u^{-3}u^{4}-6$$

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

$$u^{3}-3u^{2}+2u^{1}-6$$

Calculate u to the power of 1 and get u.

$$u^{3}-3u^{2}+2u-6$$