Solve (x-2)(x-3)(x-5)(x-4)(x-8)

$$(x-2)(x-3)(x-5)(x-4)(x-8)$$

Evaluate

$$\left(x-8\right)\left(x-5\right)\left(x-4\right)\left(x-3\right)\left(x-2\right)$$

Solution Steps

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

$$\left(x^{2}-3x-2x+6\right)\left(x-5\right)\left(x-4\right)\left(x-8\right)$$

Combine -3x and -2x to get -5x.

$$\left(x^{2}-5x+6\right)\left(x-5\right)\left(x-4\right)\left(x-8\right)$$

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

$$\left(x^{3}-5x^{2}-5x^{2}+25x+6x-30\right)\left(x-4\right)\left(x-8\right)$$

Combine -5x^{2} and -5x^{2} to get -10x^{2}.

$$\left(x^{3}-10x^{2}+25x+6x-30\right)\left(x-4\right)\left(x-8\right)$$

Combine 25x and 6x to get 31x.

$$\left(x^{3}-10x^{2}+31x-30\right)\left(x-4\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x^{3}-10x^{2}+31x-30 by each term of x-4.

$$\left(x^{4}-4x^{3}-10x^{3}+40x^{2}+31x^{2}-124x-30x+120\right)\left(x-8\right)$$

Combine -4x^{3} and -10x^{3} to get -14x^{3}.

$$\left(x^{4}-14x^{3}+40x^{2}+31x^{2}-124x-30x+120\right)\left(x-8\right)$$

Combine 40x^{2} and 31x^{2} to get 71x^{2}.

$$\left(x^{4}-14x^{3}+71x^{2}-124x-30x+120\right)\left(x-8\right)$$

Combine -124x and -30x to get -154x.

$$\left(x^{4}-14x^{3}+71x^{2}-154x+120\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x^{4}-14x^{3}+71x^{2}-154x+120 by each term of x-8.

$$x^{5}-8x^{4}-14x^{4}+112x^{3}+71x^{3}-568x^{2}-154x^{2}+1232x+120x-960$$

Combine -8x^{4} and -14x^{4} to get -22x^{4}.

$$x^{5}-22x^{4}+112x^{3}+71x^{3}-568x^{2}-154x^{2}+1232x+120x-960$$

Combine 112x^{3} and 71x^{3} to get 183x^{3}.

$$x^{5}-22x^{4}+183x^{3}-568x^{2}-154x^{2}+1232x+120x-960$$

Combine -568x^{2} and -154x^{2} to get -722x^{2}.

$$x^{5}-22x^{4}+183x^{3}-722x^{2}+1232x+120x-960$$

Combine 1232x and 120x to get 1352x.

$$x^{5}-22x^{4}+183x^{3}-722x^{2}+1352x-960$$

Expand

$$x^{5}-22x^{4}+183x^{3}-722x^{2}+1352x-960$$

Solution Steps

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

$$\left(x^{2}-3x-2x+6\right)\left(x-5\right)\left(x-4\right)\left(x-8\right)$$

Combine -3x and -2x to get -5x.

$$\left(x^{2}-5x+6\right)\left(x-5\right)\left(x-4\right)\left(x-8\right)$$

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

$$\left(x^{3}-5x^{2}-5x^{2}+25x+6x-30\right)\left(x-4\right)\left(x-8\right)$$

Combine -5x^{2} and -5x^{2} to get -10x^{2}.

$$\left(x^{3}-10x^{2}+25x+6x-30\right)\left(x-4\right)\left(x-8\right)$$

Combine 25x and 6x to get 31x.

$$\left(x^{3}-10x^{2}+31x-30\right)\left(x-4\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x^{3}-10x^{2}+31x-30 by each term of x-4.

$$\left(x^{4}-4x^{3}-10x^{3}+40x^{2}+31x^{2}-124x-30x+120\right)\left(x-8\right)$$

Combine -4x^{3} and -10x^{3} to get -14x^{3}.

$$\left(x^{4}-14x^{3}+40x^{2}+31x^{2}-124x-30x+120\right)\left(x-8\right)$$

Combine 40x^{2} and 31x^{2} to get 71x^{2}.

$$\left(x^{4}-14x^{3}+71x^{2}-124x-30x+120\right)\left(x-8\right)$$

Combine -124x and -30x to get -154x.

$$\left(x^{4}-14x^{3}+71x^{2}-154x+120\right)\left(x-8\right)$$

Apply the distributive property by multiplying each term of x^{4}-14x^{3}+71x^{2}-154x+120 by each term of x-8.

$$x^{5}-8x^{4}-14x^{4}+112x^{3}+71x^{3}-568x^{2}-154x^{2}+1232x+120x-960$$

Combine -8x^{4} and -14x^{4} to get -22x^{4}.

$$x^{5}-22x^{4}+112x^{3}+71x^{3}-568x^{2}-154x^{2}+1232x+120x-960$$

Combine 112x^{3} and 71x^{3} to get 183x^{3}.

$$x^{5}-22x^{4}+183x^{3}-568x^{2}-154x^{2}+1232x+120x-960$$

Combine -568x^{2} and -154x^{2} to get -722x^{2}.

$$x^{5}-22x^{4}+183x^{3}-722x^{2}+1232x+120x-960$$

Combine 1232x and 120x to get 1352x.

$$x^{5}-22x^{4}+183x^{3}-722x^{2}+1352x-960$$