Solve (t-1)(t+1)^2

$$( t - 1 ) ( t + 1 ) ^ { 2 }$$

Expand

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

Solution Steps

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

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

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

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

Evaluate

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

Solution Steps

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

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

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

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