Solve (x^2-1)(x+1)(x+2)(x-4)

$$( x ^ { 2 } - 1 ) ( x + 1 ) ( x + 2 ) ( x - 4 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply x^{2}-1 by x+1.

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

Use the distributive property to multiply x^{3}+x^{2}-x-1 by x+2 and combine like terms.

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

Use the distributive property to multiply x^{4}+3x^{3}+x^{2}-3x-2 by x-4 and combine like terms.

$$x^{5}-x^{4}-11x^{3}-7x^{2}+10x+8$$

Expand

$$x^{5}-x^{4}-11x^{3}-7x^{2}+10x+8$$

Solution Steps

Use the distributive property to multiply x^{2}-1 by x+1.

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

Use the distributive property to multiply x^{3}+x^{2}-x-1 by x+2 and combine like terms.

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

Use the distributive property to multiply x^{4}+3x^{3}+x^{2}-3x-2 by x-4 and combine like terms.

$$x^{5}-x^{4}-11x^{3}-7x^{2}+10x+8$$