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

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

Evaluate

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

Solution Steps

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

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

Combine 2x and x to get 3x.

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

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

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

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

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

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

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

Apply the distributive property by multiplying each term of x^{3}-7x-6 by each term of x+3.

$$x^{4}+3x^{3}-7x^{2}-21x-6x-18$$

Combine -21x and -6x to get -27x.

$$x^{4}+3x^{3}-7x^{2}-27x-18$$

Expand

$$x^{4}+3x^{3}-7x^{2}-27x-18$$

Solution Steps

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

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

Combine 2x and x to get 3x.

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

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

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

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

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

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

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

Apply the distributive property by multiplying each term of x^{3}-7x-6 by each term of x+3.

$$x^{4}+3x^{3}-7x^{2}-21x-6x-18$$

Combine -21x and -6x to get -27x.

$$x^{4}+3x^{3}-7x^{2}-27x-18$$