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

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

Evaluate

$$21-9a-2a^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+3\right)^{2}.

$$4a^{2}+12a+9-3\left(2a-1\right)\left(a+4\right)$$

Use the distributive property to multiply -3 by 2a-1.

$$4a^{2}+12a+9+\left(-6a+3\right)\left(a+4\right)$$

Use the distributive property to multiply -6a+3 by a+4 and combine like terms.

$$4a^{2}+12a+9-6a^{2}-21a+12$$

Combine 4a^{2} and -6a^{2} to get -2a^{2}.

$$-2a^{2}+12a+9-21a+12$$

Combine 12a and -21a to get -9a.

$$-2a^{2}-9a+9+12$$

Add 9 and 12 to get 21.

$$-2a^{2}-9a+21$$

Expand

$$21-9a-2a^{2}$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(2a+3\right)^{2}.

$$4a^{2}+12a+9-3\left(2a-1\right)\left(a+4\right)$$

Use the distributive property to multiply -3 by 2a-1.

$$4a^{2}+12a+9+\left(-6a+3\right)\left(a+4\right)$$

Use the distributive property to multiply -6a+3 by a+4 and combine like terms.

$$4a^{2}+12a+9-6a^{2}-21a+12$$

Combine 4a^{2} and -6a^{2} to get -2a^{2}.

$$-2a^{2}+12a+9-21a+12$$

Combine 12a and -21a to get -9a.

$$-2a^{2}-9a+9+12$$

Add 9 and 12 to get 21.

$$-2a^{2}-9a+21$$