Solve (2a+3)(2a-1)-(2a+1)^2

$$( 2 a + 3 ) ( 2 a - 1 ) - ( 2 a + 1 ) ^ { 2 }$$

Evaluate

$$-4$$

Solution Steps

Use the distributive property to multiply 2a+3 by 2a-1 and combine like terms.

$$4a^{2}+4a-3-\left(2a+1\right)^{2}$$

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

$$4a^{2}+4a-3-\left(4a^{2}+4a+1\right)$$

To find the opposite of 4a^{2}+4a+1, find the opposite of each term.

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

Combine 4a^{2} and -4a^{2} to get 0.

$$4a-3-4a-1$$

Combine 4a and -4a to get 0.

$$-3-1$$

Subtract 1 from -3 to get -4.

$$-4$$

Factor

$$-4$$