Basic Math Examples

$p^{3} - 4 p^{2} = 0$

Step 1

Factor $p^{2}$ out of $p^{3} - 4 p^{2}$ .

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Step 1.1

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

$p^{2} p - 4 p^{2} = 0$

Step 1.2

Factor $p^{2}$ out of $- 4 p^{2}$ .

$p^{2} p + p^{2} \cdot - 4 = 0$

Step 1.3

Factor $p^{2}$ out of $p^{2} p + p^{2} \cdot - 4$ .

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

Step 2

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

$p^{2} = 0$

$p - 4 = 0$

Step 3

Set $p^{2}$ equal to $0$ and solve for $p$ .

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Step 3.1

Set $p^{2}$ equal to $0$ .

$p^{2} = 0$

Step 3.2

Solve $p^{2} = 0$ for $p$ .

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Step 3.2.1

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

$p = \pm \sqrt{0}$

Step 3.2.2

Simplify $\pm \sqrt{0}$ .

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Step 3.2.2.1

Rewrite $0$ as $0^{2}$ .

$p = \pm \sqrt{0^{2}}$

Step 3.2.2.2

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

$p = \pm 0$

Step 3.2.2.3

Plus or minus $0$ is $0$ .

$p = 0$

Step 4

Set $p - 4$ equal to $0$ and solve for $p$ .

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Step 4.1

Set $p - 4$ equal to $0$ .

$p - 4 = 0$

Step 4.2

Add $4$ to both sides of the equation.

$p = 4$

Step 5

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

$p = 0, 4$