Solve (x-1)(x^2+x+1)*(x^4+x^3+x^2+x+1)

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

Evaluate

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

Solution Steps

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

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

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

$$x^{7}+x^{6}+x^{5}-x^{2}-x-1$$

Expand

$$x^{7}+x^{6}+x^{5}-x^{2}-x-1$$

Solution Steps

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

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

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

$$x^{7}+x^{6}+x^{5}-x^{2}-x-1$$