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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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