Basic Math Examples

$p = p r^{2}$

Step 1

Subtract $p r^{2}$ from both sides of the equation.

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

Step 2

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

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Step 2.1

Factor $p$ out of $p^{1}$ .

$p \cdot 1 - p r^{2} = 0$

Step 2.2

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

$p \cdot 1 + p (- 1 r^{2}) = 0$

Step 2.3

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

$p (1 - 1 r^{2}) = 0$

Step 3

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

$p (1^{2} - 1 r^{2}) = 0$

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = r$ .

$p ((1 + r) (1 - r)) = 0$

Step 4.2

Remove unnecessary parentheses.

$p (1 + r) (1 - r) = 0$

Step 5

Divide each term in $p (1 + r) (1 - r) = 0$ by $(1 + r) (1 - r)$ and simplify.

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Step 5.1

Divide each term in $p (1 + r) (1 - r) = 0$ by $(1 + r) (1 - r)$ .

$\frac{p (1 + r) (1 - r)}{(1 + r) (1 - r)} = \frac{0}{(1 + r) (1 - r)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $1 + r$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{p (1 + r) (1 - r)}{(1 + r) (1 - r)} = \frac{0}{(1 + r) (1 - r)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{p (1 - r)}{1 - r} = \frac{0}{(1 + r) (1 - r)}$

Step 5.2.2

Cancel the common factor of $1 - r$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{p (1 - r)}{1 - r} = \frac{0}{(1 + r) (1 - r)}$

Step 5.2.2.2

Divide $p$ by $1$ .

$p = \frac{0}{(1 + r) (1 - r)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $(1 + r) (1 - r)$ .

$p = 0$