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

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

Evaluate

$$\left(a-3\right)\left(3a+1\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a-1\right)^{2}.

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

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

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

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

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

Combine 4a^{2} and -a^{2} to get 3a^{2}.

$$3a^{2}-4a+1-4a-4$$

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

$$3a^{2}-8a+1-4$$

Subtract 4 from 1 to get -3.

$$3a^{2}-8a-3$$

Expand

$$3a^{2}-8a-3$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(2a-1\right)^{2}.

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

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

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

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

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

Combine 4a^{2} and -a^{2} to get 3a^{2}.

$$3a^{2}-4a+1-4a-4$$

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

$$3a^{2}-8a+1-4$$

Subtract 4 from 1 to get -3.

$$3a^{2}-8a-3$$