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

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

Evaluate

$$-12a^{3}-4a^{2}-12$$

Solution Steps

Use the distributive property to multiply 4 by a^{4}+1.

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

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

$$4a^{4}+4-\left(4a^{4}+12a^{3}+4a^{2}+16\right)$$

To find the opposite of 4a^{4}+12a^{3}+4a^{2}+16, find the opposite of each term.

$$4a^{4}+4-4a^{4}-12a^{3}-4a^{2}-16$$

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

$$4-12a^{3}-4a^{2}-16$$

Subtract 16 from 4 to get -12.

$$-12-12a^{3}-4a^{2}$$

Expand

$$-12a^{3}-4a^{2}-12$$

Solution Steps

Use the distributive property to multiply 4 by a^{4}+1.

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

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

$$4a^{4}+4-\left(4a^{4}+12a^{3}+4a^{2}+16\right)$$

To find the opposite of 4a^{4}+12a^{3}+4a^{2}+16, find the opposite of each term.

$$4a^{4}+4-4a^{4}-12a^{3}-4a^{2}-16$$

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

$$4-12a^{3}-4a^{2}-16$$

Subtract 16 from 4 to get -12.

$$-12-12a^{3}-4a^{2}$$