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

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

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

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

$$x^{3}-1=x^{3}-1$$

Subtract x^{3} from both sides.

$$x^{3}-1-x^{3}=-1$$

Combine x^{3} and -x^{3} to get 0.

$$-1=-1$$

Compare -1 and -1.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

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

$$x^{3}-1=x^{3}-1$$

Subtract x^{3} from both sides.

$$x^{3}-1-x^{3}=-1$$

Combine x^{3} and -x^{3} to get 0.

$$-1=-1$$

Compare -1 and -1.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$