Solve (1-y)(1+y)geq0

$$(1-y)(1+y) \geq 0$$

Solve for y

$$y\in \begin{bmatrix}-1,1\end{bmatrix}$$

Solution Steps

For the product to be ≥0, y+1 and 1-y have to be both ≤0 or both ≥0. Consider the case when y+1 and 1-y are both ≤0.

$$y+1\leq 0 1-y\leq 0$$

This is false for any y.

$$y\in \emptyset$$

Consider the case when y+1 and 1-y are both ≥0.

$$1-y\geq 0 y+1\geq 0$$

The solution satisfying both inequalities is y\in \left[-1,1\right].

$$y\in \begin{bmatrix}-1,1\end{bmatrix}$$

The final solution is the union of the obtained solutions.

$$y\in \begin{bmatrix}-1,1\end{bmatrix}$$