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

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

Evaluate

$$-4a-4$$

Solution Steps

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

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

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

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

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

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

Combine a^{2} and -2a^{2} to get -a^{2}.

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

Combine 4a and -8a to get -4a.

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

Subtract 8 from 4 to get -4.

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

Combine -a^{2} and a^{2} to get 0.

$$-4a-4$$

Expand

$$-4a-4$$

Solution Steps

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

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

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

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

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

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

Combine a^{2} and -2a^{2} to get -a^{2}.

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

Combine 4a and -8a to get -4a.

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

Subtract 8 from 4 to get -4.

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

Combine -a^{2} and a^{2} to get 0.

$$-4a-4$$