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

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

Evaluate

$$a^{8}-1$$

Solution Steps

Use the distributive property to multiply a-1 by a^{2}+1.

$$\left(a^{3}+a-a^{2}-1\right)\left(a+1\right)\left(a^{4}+1\right)$$

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

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

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.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$a^{8}-1$$

Expand

$$a^{8}-1$$

Solution Steps

Use the distributive property to multiply a-1 by a^{2}+1.

$$\left(a^{3}+a-a^{2}-1\right)\left(a+1\right)\left(a^{4}+1\right)$$

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

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

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.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$a^{8}-1$$