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

$$( 2 a + 4 ) \cdot ( 4 a + 2 ) - ( 2 a + 3 ) \cdot ( 3 a + 1 ) =$$

Evaluate

$$2a^{2}+9a+5$$

Solution Steps

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

$$8a^{2}+4a+16a+8-\left(2a+3\right)\left(3a+1\right)$$

Combine 4a and 16a to get 20a.

$$8a^{2}+20a+8-\left(2a+3\right)\left(3a+1\right)$$

Apply the distributive property by multiplying each term of 2a+3 by each term of 3a+1.

$$8a^{2}+20a+8-\left(6a^{2}+2a+9a+3\right)$$

Combine 2a and 9a to get 11a.

$$8a^{2}+20a+8-\left(6a^{2}+11a+3\right)$$

To find the opposite of 6a^{2}+11a+3, find the opposite of each term.

$$8a^{2}+20a+8-6a^{2}-11a-3$$

Combine 8a^{2} and -6a^{2} to get 2a^{2}.

$$2a^{2}+20a+8-11a-3$$

Combine 20a and -11a to get 9a.

$$2a^{2}+9a+8-3$$

Subtract 3 from 8 to get 5.

$$2a^{2}+9a+5$$

Expand

$$2a^{2}+9a+5$$

Solution Steps

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

$$8a^{2}+4a+16a+8-\left(2a+3\right)\left(3a+1\right)$$

Combine 4a and 16a to get 20a.

$$8a^{2}+20a+8-\left(2a+3\right)\left(3a+1\right)$$

Apply the distributive property by multiplying each term of 2a+3 by each term of 3a+1.

$$8a^{2}+20a+8-\left(6a^{2}+2a+9a+3\right)$$

Combine 2a and 9a to get 11a.

$$8a^{2}+20a+8-\left(6a^{2}+11a+3\right)$$

To find the opposite of 6a^{2}+11a+3, find the opposite of each term.

$$8a^{2}+20a+8-6a^{2}-11a-3$$

Combine 8a^{2} and -6a^{2} to get 2a^{2}.

$$2a^{2}+20a+8-11a-3$$

Combine 20a and -11a to get 9a.

$$2a^{2}+9a+8-3$$

Subtract 3 from 8 to get 5.

$$2a^{2}+9a+5$$