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

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

Evaluate

$$-2\left(x-3\right)\left(x+1\right)$$

Solution Steps

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

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

Combine 2x and -3x to get -x.

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

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

$$x^{2}-x-6-\left(3x^{2}+4x-9x-12\right)$$

Combine 4x and -9x to get -5x.

$$x^{2}-x-6-\left(3x^{2}-5x-12\right)$$

To find the opposite of 3x^{2}-5x-12, find the opposite of each term.

$$x^{2}-x-6-3x^{2}-\left(-5x\right)-\left(-12\right)$$

The opposite of -5x is 5x.

$$x^{2}-x-6-3x^{2}+5x-\left(-12\right)$$

The opposite of -12 is 12.

$$x^{2}-x-6-3x^{2}+5x+12$$

Combine x^{2} and -3x^{2} to get -2x^{2}.

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

Combine -x and 5x to get 4x.

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

Add -6 and 12 to get 6.

$$-2x^{2}+4x+6$$

Expand

$$6+4x-2x^{2}$$

Solution Steps

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

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

Combine 2x and -3x to get -x.

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

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

$$x^{2}-x-6-\left(3x^{2}+4x-9x-12\right)$$

Combine 4x and -9x to get -5x.

$$x^{2}-x-6-\left(3x^{2}-5x-12\right)$$

To find the opposite of 3x^{2}-5x-12, find the opposite of each term.

$$x^{2}-x-6-3x^{2}-\left(-5x\right)-\left(-12\right)$$

The opposite of -5x is 5x.

$$x^{2}-x-6-3x^{2}+5x-\left(-12\right)$$

The opposite of -12 is 12.

$$x^{2}-x-6-3x^{2}+5x+12$$

Combine x^{2} and -3x^{2} to get -2x^{2}.

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

Combine -x and 5x to get 4x.

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

Add -6 and 12 to get 6.

$$-2x^{2}+4x+6$$