Solve left(k+1right)left(k^2-k+1right)>k^3-2k+1

$$\left( k+1 \right) \left( { k }^{ 2 } -k+1 \right) > { k }^{ 3 } -2k+1$$

Solve for k

$$k>0$$

Solution Steps

Use the distributive property to multiply k+1 by k^{2}-k+1 and combine like terms.

$$k^{3}+1>k^{3}-2k+1$$

Subtract k^{3} from both sides.

$$k^{3}+1-k^{3}>-2k+1$$

Combine k^{3} and -k^{3} to get 0.

$$1>-2k+1$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$-2k+1<1$$

Subtract 1 from both sides.

$$-2k<1-1$$

Subtract 1 from 1 to get 0.

$$-2k<0$$

Product of two numbers is <0 if one is >0 and the other is <0. Since -2<0, k must be >0.

$$k>0$$