Solve 3a^2-(a-2)^2

$$3 a ^ { 2 } - ( a - 2 ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

Combine 3a^{2} and -a^{2} to get 2a^{2}.

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

Expand

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

Solution Steps

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

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

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

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

Combine 3a^{2} and -a^{2} to get 2a^{2}.

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