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

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

Evaluate

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

Solution Steps

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

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

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

$$x^{5}-2x^{4}-x^{3}+4x^{2}-5x+2$$

Expand

$$x^{5}-2x^{4}-x^{3}+4x^{2}-5x+2$$

Solution Steps

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

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

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

$$x^{5}-2x^{4}-x^{3}+4x^{2}-5x+2$$