Solve (x-8)(x-6)(x-3)(x+2)(x+4)

$$( x - 8 ) ( x - 6 ) ( x - 3 ) ( x + 2 ) ( x + 4 )$$

Expand

$$x^{5}-11x^{4}-4x^{3}+260x^{2}-144x-1152$$

Solution Steps

Apply the distributive property by multiplying each term of x-8 by each term of x-6.

$$\left(x^{2}-6x-8x+48\right)\left(x-3\right)\left(x+2\right)\left(x+4\right)$$

Combine -6x and -8x to get -14x.

$$\left(x^{2}-14x+48\right)\left(x-3\right)\left(x+2\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{2}-14x+48 by each term of x-3.

$$\left(x^{3}-3x^{2}-14x^{2}+42x+48x-144\right)\left(x+2\right)\left(x+4\right)$$

Combine -3x^{2} and -14x^{2} to get -17x^{2}.

$$\left(x^{3}-17x^{2}+42x+48x-144\right)\left(x+2\right)\left(x+4\right)$$

Combine 42x and 48x to get 90x.

$$\left(x^{3}-17x^{2}+90x-144\right)\left(x+2\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{3}-17x^{2}+90x-144 by each term of x+2.

$$\left(x^{4}+2x^{3}-17x^{3}-34x^{2}+90x^{2}+180x-144x-288\right)\left(x+4\right)$$

Combine 2x^{3} and -17x^{3} to get -15x^{3}.

$$\left(x^{4}-15x^{3}-34x^{2}+90x^{2}+180x-144x-288\right)\left(x+4\right)$$

Combine -34x^{2} and 90x^{2} to get 56x^{2}.

$$\left(x^{4}-15x^{3}+56x^{2}+180x-144x-288\right)\left(x+4\right)$$

Combine 180x and -144x to get 36x.

$$\left(x^{4}-15x^{3}+56x^{2}+36x-288\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{4}-15x^{3}+56x^{2}+36x-288 by each term of x+4.

$$x^{5}+4x^{4}-15x^{4}-60x^{3}+56x^{3}+224x^{2}+36x^{2}+144x-288x-1152$$

Combine 4x^{4} and -15x^{4} to get -11x^{4}.

$$x^{5}-11x^{4}-60x^{3}+56x^{3}+224x^{2}+36x^{2}+144x-288x-1152$$

Combine -60x^{3} and 56x^{3} to get -4x^{3}.

$$x^{5}-11x^{4}-4x^{3}+224x^{2}+36x^{2}+144x-288x-1152$$

Combine 224x^{2} and 36x^{2} to get 260x^{2}.

$$x^{5}-11x^{4}-4x^{3}+260x^{2}+144x-288x-1152$$

Combine 144x and -288x to get -144x.

$$x^{5}-11x^{4}-4x^{3}+260x^{2}-144x-1152$$

Evaluate

$$\left(x-8\right)\left(x-6\right)\left(x-3\right)\left(x+2\right)\left(x+4\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-8 by each term of x-6.

$$\left(x^{2}-6x-8x+48\right)\left(x-3\right)\left(x+2\right)\left(x+4\right)$$

Combine -6x and -8x to get -14x.

$$\left(x^{2}-14x+48\right)\left(x-3\right)\left(x+2\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{2}-14x+48 by each term of x-3.

$$\left(x^{3}-3x^{2}-14x^{2}+42x+48x-144\right)\left(x+2\right)\left(x+4\right)$$

Combine -3x^{2} and -14x^{2} to get -17x^{2}.

$$\left(x^{3}-17x^{2}+42x+48x-144\right)\left(x+2\right)\left(x+4\right)$$

Combine 42x and 48x to get 90x.

$$\left(x^{3}-17x^{2}+90x-144\right)\left(x+2\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{3}-17x^{2}+90x-144 by each term of x+2.

$$\left(x^{4}+2x^{3}-17x^{3}-34x^{2}+90x^{2}+180x-144x-288\right)\left(x+4\right)$$

Combine 2x^{3} and -17x^{3} to get -15x^{3}.

$$\left(x^{4}-15x^{3}-34x^{2}+90x^{2}+180x-144x-288\right)\left(x+4\right)$$

Combine -34x^{2} and 90x^{2} to get 56x^{2}.

$$\left(x^{4}-15x^{3}+56x^{2}+180x-144x-288\right)\left(x+4\right)$$

Combine 180x and -144x to get 36x.

$$\left(x^{4}-15x^{3}+56x^{2}+36x-288\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{4}-15x^{3}+56x^{2}+36x-288 by each term of x+4.

$$x^{5}+4x^{4}-15x^{4}-60x^{3}+56x^{3}+224x^{2}+36x^{2}+144x-288x-1152$$

Combine 4x^{4} and -15x^{4} to get -11x^{4}.

$$x^{5}-11x^{4}-60x^{3}+56x^{3}+224x^{2}+36x^{2}+144x-288x-1152$$

Combine -60x^{3} and 56x^{3} to get -4x^{3}.

$$x^{5}-11x^{4}-4x^{3}+224x^{2}+36x^{2}+144x-288x-1152$$

Combine 224x^{2} and 36x^{2} to get 260x^{2}.

$$x^{5}-11x^{4}-4x^{3}+260x^{2}+144x-288x-1152$$

Combine 144x and -288x to get -144x.

$$x^{5}-11x^{4}-4x^{3}+260x^{2}-144x-1152$$