Solve left(z-1right)^2left(z+1right)

$${ \left(z-1 \right) }^{ 2 } \left( z+1 \right)$$

Evaluate

$$\left(z+1\right)\left(z-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(z-1\right)^{2}.

$$\left(z^{2}-2z+1\right)\left(z+1\right)$$

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

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(z-1\right)^{2}.

$$\left(z^{2}-2z+1\right)\left(z+1\right)$$

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

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