Solve by Factoring y^3=100y

$y^{3} = 100 y$

Step 1

Subtract $100 y$ from both sides of the equation.

$y^{3} - 100 y = 0$

Step 2

Factor $y$ out of $y^{3} - 100 y$ .

Factor $y$ out of $y^{3}$ .

$y \cdot y^{2} - 100 y = 0$

Factor $y$ out of $- 100 y$ .

$y \cdot y^{2} + y \cdot - 100 = 0$

Factor $y$ out of $y \cdot y^{2} + y \cdot - 100$ .

$y (y^{2} - 100) = 0$

Step 3

Rewrite $100$ as $10^{2}$ .

$y (y^{2} - 10^{2}) = 0$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 10$ .

$y ((y + 10) (y - 10)) = 0$

Remove unnecessary parentheses.

$y (y + 10) (y - 10) = 0$

Step 5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y = 0$

$y + 10 = 0$

$y - 10 = 0$

Step 6

Set $y$ equal to $0$ .

$y = 0$

Step 7

Set $y + 10$ equal to $0$ and solve for $y$ .

Set $y + 10$ equal to $0$ .

$y + 10 = 0$

Subtract $10$ from both sides of the equation.

$y = - 10$

Step 8

Set $y - 10$ equal to $0$ and solve for $y$ .

Set $y - 10$ equal to $0$ .

$y - 10 = 0$

Add $10$ to both sides of the equation.

$y = 10$

Step 9

The final solution is all the values that make $y (y + 10) (y - 10) = 0$ true.

$y = 0, - 10, 10$