Solve (3a+1)(2a-3)+(6a-5)(a-4)

$$( 3 a + 1 ) ( 2 a - 3 ) + ( 6 a - 5 ) ( a - 4 )$$

Evaluate

$$12a^{2}-36a+17$$

Solution Steps

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

$$6a^{2}-9a+2a-3+\left(6a-5\right)\left(a-4\right)$$

Combine -9a and 2a to get -7a.

$$6a^{2}-7a-3+\left(6a-5\right)\left(a-4\right)$$

Apply the distributive property by multiplying each term of 6a-5 by each term of a-4.

$$6a^{2}-7a-3+6a^{2}-24a-5a+20$$

Combine -24a and -5a to get -29a.

$$6a^{2}-7a-3+6a^{2}-29a+20$$

Combine 6a^{2} and 6a^{2} to get 12a^{2}.

$$12a^{2}-7a-3-29a+20$$

Combine -7a and -29a to get -36a.

$$12a^{2}-36a-3+20$$

Add -3 and 20 to get 17.

$$12a^{2}-36a+17$$

Expand

$$12a^{2}-36a+17$$

Solution Steps

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

$$6a^{2}-9a+2a-3+\left(6a-5\right)\left(a-4\right)$$

Combine -9a and 2a to get -7a.

$$6a^{2}-7a-3+\left(6a-5\right)\left(a-4\right)$$

Apply the distributive property by multiplying each term of 6a-5 by each term of a-4.

$$6a^{2}-7a-3+6a^{2}-24a-5a+20$$

Combine -24a and -5a to get -29a.

$$6a^{2}-7a-3+6a^{2}-29a+20$$

Combine 6a^{2} and 6a^{2} to get 12a^{2}.

$$12a^{2}-7a-3-29a+20$$

Combine -7a and -29a to get -36a.

$$12a^{2}-36a-3+20$$

Add -3 and 20 to get 17.

$$12a^{2}-36a+17$$