Solve x^2(x^2-x+1)*(x^3-x^2+x-1)

$$x ^ { 2 } ( x ^ { 2 } - x + 1 ) \times ( x ^ { 3 } - x ^ { 2 } + x - 1 )$$

Evaluate

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

Solution Steps

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

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

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

$$x^{7}-2x^{6}+3x^{5}-3x^{4}+2x^{3}-x^{2}$$

Expand

$$x^{7}-2x^{6}+3x^{5}-3x^{4}+2x^{3}-x^{2}$$

Solution Steps

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

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

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

$$x^{7}-2x^{6}+3x^{5}-3x^{4}+2x^{3}-x^{2}$$