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

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

Evaluate

$$\left(x-9\right)\left(x+2\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+4 by each term of x-3.

$$2x^{2}-6x+4x-12-\left(x+3\right)\left(x+2\right)$$

Combine -6x and 4x to get -2x.

$$2x^{2}-2x-12-\left(x+3\right)\left(x+2\right)$$

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

$$2x^{2}-2x-12-\left(x^{2}+2x+3x+6\right)$$

Combine 2x and 3x to get 5x.

$$2x^{2}-2x-12-\left(x^{2}+5x+6\right)$$

To find the opposite of x^{2}+5x+6, find the opposite of each term.

$$2x^{2}-2x-12-x^{2}-5x-6$$

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

$$x^{2}-2x-12-5x-6$$

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

$$x^{2}-7x-12-6$$

Subtract 6 from -12 to get -18.

$$x^{2}-7x-18$$

Expand

$$x^{2}-7x-18$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+4 by each term of x-3.

$$2x^{2}-6x+4x-12-\left(x+3\right)\left(x+2\right)$$

Combine -6x and 4x to get -2x.

$$2x^{2}-2x-12-\left(x+3\right)\left(x+2\right)$$

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

$$2x^{2}-2x-12-\left(x^{2}+2x+3x+6\right)$$

Combine 2x and 3x to get 5x.

$$2x^{2}-2x-12-\left(x^{2}+5x+6\right)$$

To find the opposite of x^{2}+5x+6, find the opposite of each term.

$$2x^{2}-2x-12-x^{2}-5x-6$$

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

$$x^{2}-2x-12-5x-6$$

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

$$x^{2}-7x-12-6$$

Subtract 6 from -12 to get -18.

$$x^{2}-7x-18$$