Solve (a-1)^3(a+1)^2=

$$( a - 1 ) ^ { 3 } ( a + 1 ) ^ { 2 } =$$

Evaluate

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

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(a-1\right)^{3}.

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

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+1\right)^{2}.

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

Use the distributive property to multiply a^{3}-3a^{2}+3a-1 by a^{2}+2a+1 and combine like terms.

$$a^{5}-a^{4}-2a^{3}+2a^{2}+a-1$$

Expand

$$a^{5}-a^{4}-2a^{3}+2a^{2}+a-1$$

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(a-1\right)^{3}.

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

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+1\right)^{2}.

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

Use the distributive property to multiply a^{3}-3a^{2}+3a-1 by a^{2}+2a+1 and combine like terms.

$$a^{5}-a^{4}-2a^{3}+2a^{2}+a-1$$