Solve (6-x)(x+2)(x-1)(x-8)(x+1)

$$( 6 - x ) ( x + 2 ) ( x - 1 ) ( x - 8 ) ( x + 1 )$$

Evaluate

$$\left(6-x\right)\left(x-8\right)\left(x+2\right)\left(x^{2}-1\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 6-x by each term of x+2.

$$\left(6x+12-x^{2}-2x\right)\left(x-1\right)\left(x-8\right)\left(x+1\right)$$

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

$$\left(4x+12-x^{2}\right)\left(x-1\right)\left(x-8\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 4x+12-x^{2} by each term of x-1.

$$\left(4x^{2}-4x+12x-12-x^{3}+x^{2}\right)\left(x-8\right)\left(x+1\right)$$

Combine -4x and 12x to get 8x.

$$\left(4x^{2}+8x-12-x^{3}+x^{2}\right)\left(x-8\right)\left(x+1\right)$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$\left(5x^{2}+8x-12-x^{3}\right)\left(x-8\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 5x^{2}+8x-12-x^{3} by each term of x-8.

$$\left(5x^{3}-40x^{2}+8x^{2}-64x-12x+96-x^{4}+8x^{3}\right)\left(x+1\right)$$

Combine -40x^{2} and 8x^{2} to get -32x^{2}.

$$\left(5x^{3}-32x^{2}-64x-12x+96-x^{4}+8x^{3}\right)\left(x+1\right)$$

Combine -64x and -12x to get -76x.

$$\left(5x^{3}-32x^{2}-76x+96-x^{4}+8x^{3}\right)\left(x+1\right)$$

Combine 5x^{3} and 8x^{3} to get 13x^{3}.

$$\left(13x^{3}-32x^{2}-76x+96-x^{4}\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 13x^{3}-32x^{2}-76x+96-x^{4} by each term of x+1.

$$13x^{4}+13x^{3}-32x^{3}-32x^{2}-76x^{2}-76x+96x+96-x^{5}-x^{4}$$

Combine 13x^{3} and -32x^{3} to get -19x^{3}.

$$13x^{4}-19x^{3}-32x^{2}-76x^{2}-76x+96x+96-x^{5}-x^{4}$$

Combine -32x^{2} and -76x^{2} to get -108x^{2}.

$$13x^{4}-19x^{3}-108x^{2}-76x+96x+96-x^{5}-x^{4}$$

Combine -76x and 96x to get 20x.

$$13x^{4}-19x^{3}-108x^{2}+20x+96-x^{5}-x^{4}$$

Combine 13x^{4} and -x^{4} to get 12x^{4}.

$$12x^{4}-19x^{3}-108x^{2}+20x+96-x^{5}$$

Expand

$$96+20x-108x^{2}-19x^{3}+12x^{4}-x^{5}$$

Solution Steps

Apply the distributive property by multiplying each term of 6-x by each term of x+2.

$$\left(6x+12-x^{2}-2x\right)\left(x-1\right)\left(x-8\right)\left(x+1\right)$$

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

$$\left(4x+12-x^{2}\right)\left(x-1\right)\left(x-8\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 4x+12-x^{2} by each term of x-1.

$$\left(4x^{2}-4x+12x-12-x^{3}+x^{2}\right)\left(x-8\right)\left(x+1\right)$$

Combine -4x and 12x to get 8x.

$$\left(4x^{2}+8x-12-x^{3}+x^{2}\right)\left(x-8\right)\left(x+1\right)$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$\left(5x^{2}+8x-12-x^{3}\right)\left(x-8\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 5x^{2}+8x-12-x^{3} by each term of x-8.

$$\left(5x^{3}-40x^{2}+8x^{2}-64x-12x+96-x^{4}+8x^{3}\right)\left(x+1\right)$$

Combine -40x^{2} and 8x^{2} to get -32x^{2}.

$$\left(5x^{3}-32x^{2}-64x-12x+96-x^{4}+8x^{3}\right)\left(x+1\right)$$

Combine -64x and -12x to get -76x.

$$\left(5x^{3}-32x^{2}-76x+96-x^{4}+8x^{3}\right)\left(x+1\right)$$

Combine 5x^{3} and 8x^{3} to get 13x^{3}.

$$\left(13x^{3}-32x^{2}-76x+96-x^{4}\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 13x^{3}-32x^{2}-76x+96-x^{4} by each term of x+1.

$$13x^{4}+13x^{3}-32x^{3}-32x^{2}-76x^{2}-76x+96x+96-x^{5}-x^{4}$$

Combine 13x^{3} and -32x^{3} to get -19x^{3}.

$$13x^{4}-19x^{3}-32x^{2}-76x^{2}-76x+96x+96-x^{5}-x^{4}$$

Combine -32x^{2} and -76x^{2} to get -108x^{2}.

$$13x^{4}-19x^{3}-108x^{2}-76x+96x+96-x^{5}-x^{4}$$

Combine -76x and 96x to get 20x.

$$13x^{4}-19x^{3}-108x^{2}+20x+96-x^{5}-x^{4}$$

Combine 13x^{4} and -x^{4} to get 12x^{4}.

$$12x^{4}-19x^{3}-108x^{2}+20x+96-x^{5}$$