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

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

Evaluate

$$a^{8}-256$$

Solution Steps

Use the distributive property to multiply a^{2}+4 by a-2.

$$\left(a^{3}-2a^{2}+4a-8\right)\left(a^{4}+16\right)\left(a+2\right)$$

Use the distributive property to multiply a^{3}-2a^{2}+4a-8 by a^{4}+16.

$$\left(a^{7}+16a^{3}-2a^{6}-32a^{2}+4a^{5}+64a-8a^{4}-128\right)\left(a+2\right)$$

Use the distributive property to multiply a^{7}+16a^{3}-2a^{6}-32a^{2}+4a^{5}+64a-8a^{4}-128 by a+2 and combine like terms.

$$a^{8}-256$$

Expand

$$a^{8}-256$$

Solution Steps

Use the distributive property to multiply a^{2}+4 by a-2.

$$\left(a^{3}-2a^{2}+4a-8\right)\left(a^{4}+16\right)\left(a+2\right)$$

Use the distributive property to multiply a^{3}-2a^{2}+4a-8 by a^{4}+16.

$$\left(a^{7}+16a^{3}-2a^{6}-32a^{2}+4a^{5}+64a-8a^{4}-128\right)\left(a+2\right)$$

Use the distributive property to multiply a^{7}+16a^{3}-2a^{6}-32a^{2}+4a^{5}+64a-8a^{4}-128 by a+2 and combine like terms.

$$a^{8}-256$$