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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply a-1 by a+1 and combine like terms.

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

Multiply a^{2}-1 and a^{2}-1 to get \left(a^{2}-1\right)^{2}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Expand

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

Solution Steps

Use the distributive property to multiply a-1 by a+1 and combine like terms.

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

Multiply a^{2}-1 and a^{2}-1 to get \left(a^{2}-1\right)^{2}.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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