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

$$( 2 a + 4 ) ( a - 3 ) - ( 2 a + 4 ) ( 2 a - 1 )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of 2a+4 by each term of a-3.

$$2a^{2}-6a+4a-12-\left(2a+4\right)\left(2a-1\right)$$

Combine -6a and 4a to get -2a.

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

Apply the distributive property by multiplying each term of 2a+4 by each term of 2a-1.

$$2a^{2}-2a-12-\left(4a^{2}-2a+8a-4\right)$$

Combine -2a and 8a to get 6a.

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

To find the opposite of 4a^{2}+6a-4, find the opposite of each term.

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

The opposite of -4 is 4.

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

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

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

Combine -2a and -6a to get -8a.

$$-2a^{2}-8a-12+4$$

Add -12 and 4 to get -8.

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

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of 2a+4 by each term of a-3.

$$2a^{2}-6a+4a-12-\left(2a+4\right)\left(2a-1\right)$$

Combine -6a and 4a to get -2a.

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

Apply the distributive property by multiplying each term of 2a+4 by each term of 2a-1.

$$2a^{2}-2a-12-\left(4a^{2}-2a+8a-4\right)$$

Combine -2a and 8a to get 6a.

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

To find the opposite of 4a^{2}+6a-4, find the opposite of each term.

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

The opposite of -4 is 4.

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

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

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

Combine -2a and -6a to get -8a.

$$-2a^{2}-8a-12+4$$

Add -12 and 4 to get -8.

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