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

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

Solve for y

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

Solution Steps

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

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

Use the distributive property to multiply \left(-x^{2}\right)x+2\left(-x^{2}\right) by x-2 and combine like terms.

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

Multiply -4 and -1 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Solve for x (complex solution)

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

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

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

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

Solve for x

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