Solve left(6x-5right)left(3x+8right)-(6x-7)(3x+6)

$$\left( 6x-5 \right) \left( 3x+8 \right) -(6x-7)(3x+6)$$

Evaluate

$$18x+2$$

Solution Steps

Apply the distributive property by multiplying each term of 6x-5 by each term of 3x+8.

$$18x^{2}+48x-15x-40-\left(6x-7\right)\left(3x+6\right)$$

Combine 48x and -15x to get 33x.

$$18x^{2}+33x-40-\left(6x-7\right)\left(3x+6\right)$$

Apply the distributive property by multiplying each term of 6x-7 by each term of 3x+6.

$$18x^{2}+33x-40-\left(18x^{2}+36x-21x-42\right)$$

Combine 36x and -21x to get 15x.

$$18x^{2}+33x-40-\left(18x^{2}+15x-42\right)$$

To find the opposite of 18x^{2}+15x-42, find the opposite of each term.

$$18x^{2}+33x-40-18x^{2}-15x-\left(-42\right)$$

The opposite of -42 is 42.

$$18x^{2}+33x-40-18x^{2}-15x+42$$

Combine 18x^{2} and -18x^{2} to get 0.

$$33x-40-15x+42$$

Combine 33x and -15x to get 18x.

$$18x-40+42$$

Add -40 and 42 to get 2.

$$18x+2$$

Expand

$$18x+2$$

Solution Steps

Apply the distributive property by multiplying each term of 6x-5 by each term of 3x+8.

$$18x^{2}+48x-15x-40-\left(6x-7\right)\left(3x+6\right)$$

Combine 48x and -15x to get 33x.

$$18x^{2}+33x-40-\left(6x-7\right)\left(3x+6\right)$$

Apply the distributive property by multiplying each term of 6x-7 by each term of 3x+6.

$$18x^{2}+33x-40-\left(18x^{2}+36x-21x-42\right)$$

Combine 36x and -21x to get 15x.

$$18x^{2}+33x-40-\left(18x^{2}+15x-42\right)$$

To find the opposite of 18x^{2}+15x-42, find the opposite of each term.

$$18x^{2}+33x-40-18x^{2}-15x-\left(-42\right)$$

The opposite of -42 is 42.

$$18x^{2}+33x-40-18x^{2}-15x+42$$

Combine 18x^{2} and -18x^{2} to get 0.

$$33x-40-15x+42$$

Combine 33x and -15x to get 18x.

$$18x-40+42$$

Add -40 and 42 to get 2.

$$18x+2$$