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

$$( x - 1 ) \cdot ( x + 1 ) \cdot ( x ^ { 2 } + x + 1 ) \cdot ( x ^ { 2 } + 1 ) ( x ^ { 2 } - x + 1 )$$

Evaluate

$$x^{8}+x^{6}-x^{2}-1$$

Solution Steps

Use the distributive property to multiply x-1 by x+1 and combine like terms.

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

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

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

Use the distributive property to multiply x^{4}+x^{3}-x-1 by x^{2}+1 and combine like terms.

$$\left(x^{6}+x^{4}+x^{5}-x-x^{2}-1\right)\left(x^{2}-x+1\right)$$

Use the distributive property to multiply x^{6}+x^{4}+x^{5}-x-x^{2}-1 by x^{2}-x+1 and combine like terms.

$$x^{8}+x^{6}-x^{2}-1$$

Expand

$$x^{8}+x^{6}-x^{2}-1$$

Solution Steps

Use the distributive property to multiply x-1 by x+1 and combine like terms.

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

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

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

Use the distributive property to multiply x^{4}+x^{3}-x-1 by x^{2}+1 and combine like terms.

$$\left(x^{6}+x^{4}+x^{5}-x-x^{2}-1\right)\left(x^{2}-x+1\right)$$

Use the distributive property to multiply x^{6}+x^{4}+x^{5}-x-x^{2}-1 by x^{2}-x+1 and combine like terms.

$$x^{8}+x^{6}-x^{2}-1$$