Solve (a^2-2)(a^2+2)(4+a^4)(a^8+16)

$$( a ^ { 2 } - 2 ) ( a ^ { 2 } + 2 ) ( 4 + a ^ { 4 } ) ( a ^ { 8 } + 16 )$$

Evaluate

$$a^{16}-256$$

Solution Steps

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

$$\left(a^{4}-4\right)\left(4+a^{4}\right)\left(a^{8}+16\right)$$

Use the distributive property to multiply a^{4}-4 by 4+a^{4} and combine like terms.

$$\left(a^{8}-16\right)\left(a^{8}+16\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 16.

$$\left(a^{8}\right)^{2}-256$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$a^{16}-256$$

Expand

$$a^{16}-256$$

Solution Steps

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

$$\left(a^{4}-4\right)\left(4+a^{4}\right)\left(a^{8}+16\right)$$

Use the distributive property to multiply a^{4}-4 by 4+a^{4} and combine like terms.

$$\left(a^{8}-16\right)\left(a^{8}+16\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 16.

$$\left(a^{8}\right)^{2}-256$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$a^{16}-256$$