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

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

Evaluate

$$-2$$

Solution Steps

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

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

Consider \left(x^{2}-1\right)\left(x^{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.

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

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

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

To find the opposite of x^{4}+1, find the opposite of each term.

$$x^{4}-1-x^{4}-1$$

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

$$-1-1$$

Subtract 1 from -1 to get -2.

$$-2$$

Factor

$$-2$$