Solve (a-1)(a+1)(a^2+1)-(a^4-1)

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

Evaluate

$$0$$

Solution Steps

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

$$\left(a^{2}-1\right)\left(a^{2}+1\right)-\left(a^{4}-1\right)$$

Consider \left(a^{2}-1\right)\left(a^{2}+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$\left(a^{2}\right)^{2}-1-\left(a^{4}-1\right)$$

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

$$a^{4}-1-\left(a^{4}-1\right)$$

To find the opposite of a^{4}-1, find the opposite of each term.

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

Combine a^{4} and -a^{4} to get 0.

$$-1+1$$

Add -1 and 1 to get 0.

$$0$$

Factor

$$0$$