Solve (x-1)(x-2)(x+3)-(x+1)(x+2)(x-3)

$$( x - 1 ) ( x - 2 ) ( x + 3 ) - ( x + 1 ) ( x + 2 ) ( x - 3 )$$

Evaluate

$$12$$

Solution Steps

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

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

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

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

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

$$x^{3}+3x^{2}-3x^{2}-9x+2x+6-\left(x+1\right)\left(x+2\right)\left(x-3\right)$$

Combine 3x^{2} and -3x^{2} to get 0.

$$x^{3}-9x+2x+6-\left(x+1\right)\left(x+2\right)\left(x-3\right)$$

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

$$x^{3}-7x+6-\left(x+1\right)\left(x+2\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x+1 by each term of x+2.

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

Combine 2x and x to get 3x.

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

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

$$x^{3}-7x+6-\left(x^{3}-3x^{2}+3x^{2}-9x+2x-6\right)$$

Combine -3x^{2} and 3x^{2} to get 0.

$$x^{3}-7x+6-\left(x^{3}-9x+2x-6\right)$$

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

$$x^{3}-7x+6-\left(x^{3}-7x-6\right)$$

To find the opposite of x^{3}-7x-6, find the opposite of each term.

$$x^{3}-7x+6-x^{3}-\left(-7x\right)-\left(-6\right)$$

The opposite of -7x is 7x.

$$x^{3}-7x+6-x^{3}+7x-\left(-6\right)$$

The opposite of -6 is 6.

$$x^{3}-7x+6-x^{3}+7x+6$$

Combine x^{3} and -x^{3} to get 0.

$$-7x+6+7x+6$$

Combine -7x and 7x to get 0.

$$6+6$$

Add 6 and 6 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$