Solve (2a-5)(a-1)+(3a+4)(2a+1)-3

$$( 2 a - 5 ) ( a - 1 ) + ( 3 a + 4 ) ( 2 a + 1 ) - 3$$

Evaluate

$$8a^{2}+4a+6$$

Solution Steps

Apply the distributive property by multiplying each term of 2a-5 by each term of a-1.

$$2a^{2}-2a-5a+5+\left(3a+4\right)\left(2a+1\right)-3$$

Combine -2a and -5a to get -7a.

$$2a^{2}-7a+5+\left(3a+4\right)\left(2a+1\right)-3$$

Apply the distributive property by multiplying each term of 3a+4 by each term of 2a+1.

$$2a^{2}-7a+5+6a^{2}+3a+8a+4-3$$

Combine 3a and 8a to get 11a.

$$2a^{2}-7a+5+6a^{2}+11a+4-3$$

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

$$8a^{2}-7a+5+11a+4-3$$

Combine -7a and 11a to get 4a.

$$8a^{2}+4a+5+4-3$$

Add 5 and 4 to get 9.

$$8a^{2}+4a+9-3$$

Subtract 3 from 9 to get 6.

$$8a^{2}+4a+6$$

Expand

$$8a^{2}+4a+6$$

Solution Steps

Apply the distributive property by multiplying each term of 2a-5 by each term of a-1.

$$2a^{2}-2a-5a+5+\left(3a+4\right)\left(2a+1\right)-3$$

Combine -2a and -5a to get -7a.

$$2a^{2}-7a+5+\left(3a+4\right)\left(2a+1\right)-3$$

Apply the distributive property by multiplying each term of 3a+4 by each term of 2a+1.

$$2a^{2}-7a+5+6a^{2}+3a+8a+4-3$$

Combine 3a and 8a to get 11a.

$$2a^{2}-7a+5+6a^{2}+11a+4-3$$

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

$$8a^{2}-7a+5+11a+4-3$$

Combine -7a and 11a to get 4a.

$$8a^{2}+4a+5+4-3$$

Add 5 and 4 to get 9.

$$8a^{2}+4a+9-3$$

Subtract 3 from 9 to get 6.

$$8a^{2}+4a+6$$