Basic Math Examples

$2 y^{3} = 8 y$

Step 1

Subtract $8 y$ from both sides of the equation.

$2 y^{3} - 8 y = 0$

Step 2

Factor the left side of the equation.

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Step 2.1

Factor $2 y$ out of $2 y^{3} - 8 y$ .

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Step 2.1.1

Factor $2 y$ out of $2 y^{3}$ .

$2 y (y^{2}) - 8 y = 0$

Step 2.1.2

Factor $2 y$ out of $- 8 y$ .

$2 y (y^{2}) + 2 y (- 4) = 0$

Step 2.1.3

Factor $2 y$ out of $2 y (y^{2}) + 2 y (- 4)$ .

$2 y (y^{2} - 4) = 0$

Step 2.2

Rewrite $4$ as $2^{2}$ .

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

Step 2.3

Factor.

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Step 2.3.1

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 $b = 2$ .

$2 y ((y + 2) (y - 2)) = 0$

Step 2.3.2

Remove unnecessary parentheses.

$2 y (y + 2) (y - 2) = 0$

Step 3

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

$y = 0$

$y + 2 = 0$

$y - 2 = 0$

Step 4

Set $y$ equal to $0$ .

$y = 0$

Step 5

Set $y + 2$ equal to $0$ and solve for $y$ .

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Step 5.1

Set $y + 2$ equal to $0$ .

$y + 2 = 0$

Step 5.2

Subtract $2$ from both sides of the equation.

$y = - 2$

Step 6

Set $y - 2$ equal to $0$ and solve for $y$ .

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Step 6.1

Set $y - 2$ equal to $0$ .

$y - 2 = 0$

Step 6.2

Add $2$ to both sides of the equation.

$y = 2$

Step 7

The final solution is all the values that make $2 y (y + 2) (y - 2) = 0$ true.

$y = 0, - 2, 2$