Solve by Factoring 4t^6-t^4=0

$4 t^{6} - t^{4} = 0$

Step 1

Factor $t^{4}$ out of $4 t^{6} - t^{4}$ .

Factor $t^{4}$ out of $4 t^{6}$ .

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

Factor $t^{4}$ out of $- t^{4}$ .

$t^{4} (4 t^{2}) + t^{4} \cdot - 1 = 0$

Factor $t^{4}$ out of $t^{4} (4 t^{2}) + t^{4} \cdot - 1$ .

$t^{4} (4 t^{2} - 1) = 0$

Step 2

Rewrite $4 t^{2}$ as ${(2 t)}^{2}$ .

$t^{4} ({(2 t)}^{2} - 1) = 0$

Step 3

Rewrite $1$ as $1^{2}$ .

$t^{4} ({(2 t)}^{2} - 1^{2}) = 0$

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 $a = 2 t$ and $b = 1$ .

$t^{4} ((2 t + 1) (2 t - 1)) = 0$

Remove unnecessary parentheses.

$t^{4} (2 t + 1) (2 t - 1) = 0$

Step 5

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

$t^{4} = 0$

$2 t + 1 = 0$

$2 t - 1 = 0$

Step 6

Set $t^{4}$ equal to $0$ and solve for $t$ .

Set $t^{4}$ equal to $0$ .

$t^{4} = 0$

Solve $t^{4} = 0$ for $t$ .

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$t = \pm \sqrt[4]{0}$

Simplify $\pm \sqrt[4]{0}$ .

Rewrite $0$ as $0^{4}$ .

$t = \pm \sqrt[4]{0^{4}}$

Pull terms out from under the radical, assuming positive real numbers.

$t = \pm 0$

Plus or minus $0$ is $0$ .

$t = 0$

Step 7

Set $2 t + 1$ equal to $0$ and solve for $t$ .

Set $2 t + 1$ equal to $0$ .

$2 t + 1 = 0$

Solve $2 t + 1 = 0$ for $t$ .

Subtract $1$ from both sides of the equation.

$2 t = - 1$

Divide each term in $2 t = - 1$ by $2$ and simplify.

Divide each term in $2 t = - 1$ by $2$ .

$\frac{2 t}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 t}{2} = \frac{- 1}{2}$

Divide $t$ by $1$ .

$t = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$t = - \frac{1}{2}$

Step 8

Set $2 t - 1$ equal to $0$ and solve for $t$ .

Set $2 t - 1$ equal to $0$ .

$2 t - 1 = 0$

Solve $2 t - 1 = 0$ for $t$ .

Add $1$ to both sides of the equation.

$2 t = 1$

Divide each term in $2 t = 1$ by $2$ and simplify.

Divide each term in $2 t = 1$ by $2$ .

$\frac{2 t}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 t}{2} = \frac{1}{2}$

Divide $t$ by $1$ .

$t = \frac{1}{2}$

Step 9

The final solution is all the values that make $t^{4} (2 t + 1) (2 t - 1) = 0$ true.

$t = 0, - \frac{1}{2}, \frac{1}{2}$

Solve by Factoring 4t^6-t^4=0

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