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

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

Solve for y

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

Solution Steps

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

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

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

$$y=x^{4}-x^{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2\sqrt{4y+1}+2}}{2}$$

$$x=\frac{\sqrt{2\sqrt{4y+1}+2}}{2}$$

$$x=\frac{\sqrt{-2\sqrt{4y+1}+2}}{2}$$

$$x=-\frac{\sqrt{-2\sqrt{4y+1}+2}}{2}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{2\sqrt{4y+1}+2}}{2}\text{; }x=-\frac{\sqrt{2\sqrt{4y+1}+2}}{2}\text{, }&y\geq -\frac{1}{4}\\x=\frac{\sqrt{-2\sqrt{4y+1}+2}}{2}\text{; }x=-\frac{\sqrt{-2\sqrt{4y+1}+2}}{2}\text{, }&y\geq -\frac{1}{4}\text{ and }y\leq 0\end{matrix}\right.$$