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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x-4.

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

Combine -4x and -2x to get -6x.

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

Apply the distributive property by multiplying each term of x^{2}-6x+8 by each term of x-6.

$$\left(x^{3}-6x^{2}-6x^{2}+36x+8x-48\right)\left(x-8\right)$$

Combine -6x^{2} and -6x^{2} to get -12x^{2}.

$$\left(x^{3}-12x^{2}+36x+8x-48\right)\left(x-8\right)$$

Combine 36x and 8x to get 44x.

$$\left(x^{3}-12x^{2}+44x-48\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x^{3}-12x^{2}+44x-48 by each term of x-8.

$$x^{4}-8x^{3}-12x^{3}+96x^{2}+44x^{2}-352x-48x+384$$

Combine -8x^{3} and -12x^{3} to get -20x^{3}.

$$x^{4}-20x^{3}+96x^{2}+44x^{2}-352x-48x+384$$

Combine 96x^{2} and 44x^{2} to get 140x^{2}.

$$x^{4}-20x^{3}+140x^{2}-352x-48x+384$$

Combine -352x and -48x to get -400x.

$$x^{4}-20x^{3}+140x^{2}-400x+384$$

Expand

$$x^{4}-20x^{3}+140x^{2}-400x+384$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x-4.

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

Combine -4x and -2x to get -6x.

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

Apply the distributive property by multiplying each term of x^{2}-6x+8 by each term of x-6.

$$\left(x^{3}-6x^{2}-6x^{2}+36x+8x-48\right)\left(x-8\right)$$

Combine -6x^{2} and -6x^{2} to get -12x^{2}.

$$\left(x^{3}-12x^{2}+36x+8x-48\right)\left(x-8\right)$$

Combine 36x and 8x to get 44x.

$$\left(x^{3}-12x^{2}+44x-48\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x^{3}-12x^{2}+44x-48 by each term of x-8.

$$x^{4}-8x^{3}-12x^{3}+96x^{2}+44x^{2}-352x-48x+384$$

Combine -8x^{3} and -12x^{3} to get -20x^{3}.

$$x^{4}-20x^{3}+96x^{2}+44x^{2}-352x-48x+384$$

Combine 96x^{2} and 44x^{2} to get 140x^{2}.

$$x^{4}-20x^{3}+140x^{2}-352x-48x+384$$

Combine -352x and -48x to get -400x.

$$x^{4}-20x^{3}+140x^{2}-400x+384$$