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

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

Evaluate

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

Solution Steps

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

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

Combine 3x and 2x to get 5x.

$$\left(x^{2}+5x+6\right)\left(x-3\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{2}+5x+6 by each term of x-3.

$$\left(x^{3}-3x^{2}+5x^{2}-15x+6x-18\right)\left(x-4\right)$$

Combine -3x^{2} and 5x^{2} to get 2x^{2}.

$$\left(x^{3}+2x^{2}-15x+6x-18\right)\left(x-4\right)$$

Combine -15x and 6x to get -9x.

$$\left(x^{3}+2x^{2}-9x-18\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{3}+2x^{2}-9x-18 by each term of x-4.

$$x^{4}-4x^{3}+2x^{3}-8x^{2}-9x^{2}+36x-18x+72$$

Combine -4x^{3} and 2x^{3} to get -2x^{3}.

$$x^{4}-2x^{3}-8x^{2}-9x^{2}+36x-18x+72$$

Combine -8x^{2} and -9x^{2} to get -17x^{2}.

$$x^{4}-2x^{3}-17x^{2}+36x-18x+72$$

Combine 36x and -18x to get 18x.

$$x^{4}-2x^{3}-17x^{2}+18x+72$$

Expand

$$x^{4}-2x^{3}-17x^{2}+18x+72$$

Solution Steps

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

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

Combine 3x and 2x to get 5x.

$$\left(x^{2}+5x+6\right)\left(x-3\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{2}+5x+6 by each term of x-3.

$$\left(x^{3}-3x^{2}+5x^{2}-15x+6x-18\right)\left(x-4\right)$$

Combine -3x^{2} and 5x^{2} to get 2x^{2}.

$$\left(x^{3}+2x^{2}-15x+6x-18\right)\left(x-4\right)$$

Combine -15x and 6x to get -9x.

$$\left(x^{3}+2x^{2}-9x-18\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{3}+2x^{2}-9x-18 by each term of x-4.

$$x^{4}-4x^{3}+2x^{3}-8x^{2}-9x^{2}+36x-18x+72$$

Combine -4x^{3} and 2x^{3} to get -2x^{3}.

$$x^{4}-2x^{3}-8x^{2}-9x^{2}+36x-18x+72$$

Combine -8x^{2} and -9x^{2} to get -17x^{2}.

$$x^{4}-2x^{3}-17x^{2}+36x-18x+72$$

Combine 36x and -18x to get 18x.

$$x^{4}-2x^{3}-17x^{2}+18x+72$$