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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a^{2}-4\right)^{2}.

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

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

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

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+2\right)^{2}.

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

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

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

Combine -8a^{2} and -4a^{2} to get -12a^{2}.

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

Subtract 16 from 16 to get 0.

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

Expand

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

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a^{2}-4\right)^{2}.

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

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

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

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+2\right)^{2}.

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

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

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

Combine -8a^{2} and -4a^{2} to get -12a^{2}.

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

Subtract 16 from 16 to get 0.

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