Solve 4(a-1)^2-(2a+1)(2a-3)

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

Evaluate

$$7-4a$$

Solution Steps

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

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

Use the distributive property to multiply 4 by a^{2}-2a+1.

$$4a^{2}-8a+4-\left(2a+1\right)\left(2a-3\right)$$

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

$$4a^{2}-8a+4-\left(4a^{2}-4a-3\right)$$

To find the opposite of 4a^{2}-4a-3, find the opposite of each term.

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

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

$$-8a+4+4a+3$$

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

$$-4a+4+3$$

Add 4 and 3 to get 7.

$$-4a+7$$

Expand

$$7-4a$$

Solution Steps

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

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

Use the distributive property to multiply 4 by a^{2}-2a+1.

$$4a^{2}-8a+4-\left(2a+1\right)\left(2a-3\right)$$

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

$$4a^{2}-8a+4-\left(4a^{2}-4a-3\right)$$

To find the opposite of 4a^{2}-4a-3, find the opposite of each term.

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

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

$$-8a+4+4a+3$$

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

$$-4a+4+3$$

Add 4 and 3 to get 7.

$$-4a+7$$