Solve =(2x+3)(x-2)-(4x+6)(x+2)

$$= ( 2 x + 3 ) ( x - 2 ) - ( 4 x + 6 ) ( x + 2 )$$

Evaluate

$$-\left(x+6\right)\left(2x+3\right)$$

Solution Steps

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

$$2x^{2}-4x+3x-6-\left(4x+6\right)\left(x+2\right)$$

Combine -4x and 3x to get -x.

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

Apply the distributive property by multiplying each term of 4x+6 by each term of x+2.

$$2x^{2}-x-6-\left(4x^{2}+8x+6x+12\right)$$

Combine 8x and 6x to get 14x.

$$2x^{2}-x-6-\left(4x^{2}+14x+12\right)$$

To find the opposite of 4x^{2}+14x+12, find the opposite of each term.

$$2x^{2}-x-6-4x^{2}-14x-12$$

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

$$-2x^{2}-x-6-14x-12$$

Combine -x and -14x to get -15x.

$$-2x^{2}-15x-6-12$$

Subtract 12 from -6 to get -18.

$$-2x^{2}-15x-18$$

Expand

$$-2x^{2}-15x-18$$

Solution Steps

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

$$2x^{2}-4x+3x-6-\left(4x+6\right)\left(x+2\right)$$

Combine -4x and 3x to get -x.

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

Apply the distributive property by multiplying each term of 4x+6 by each term of x+2.

$$2x^{2}-x-6-\left(4x^{2}+8x+6x+12\right)$$

Combine 8x and 6x to get 14x.

$$2x^{2}-x-6-\left(4x^{2}+14x+12\right)$$

To find the opposite of 4x^{2}+14x+12, find the opposite of each term.

$$2x^{2}-x-6-4x^{2}-14x-12$$

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

$$-2x^{2}-x-6-14x-12$$

Combine -x and -14x to get -15x.

$$-2x^{2}-15x-6-12$$

Subtract 12 from -6 to get -18.

$$-2x^{2}-15x-18$$