Solve (x-3)(x+1)(x+2)(x+6)

$$( x - 3 ) ( x + 1 ) ( x + 2 ) ( x + 6 )$$

Expand

$$x^{4}+6x^{3}-7x^{2}-48x-36$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x+1.

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

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

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

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

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

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

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

Combine -4x and -3x to get -7x.

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

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

$$x^{4}+6x^{3}-7x^{2}-42x-6x-36$$

Combine -42x and -6x to get -48x.

$$x^{4}+6x^{3}-7x^{2}-48x-36$$

Evaluate

$$\left(x-3\right)\left(x+1\right)\left(x+2\right)\left(x+6\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x+1.

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

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

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

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

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

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

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

Combine -4x and -3x to get -7x.

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

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

$$x^{4}+6x^{3}-7x^{2}-42x-6x-36$$

Combine -42x and -6x to get -48x.

$$x^{4}+6x^{3}-7x^{2}-48x-36$$