Basic Math Examples

$\frac{m^{2} - n^{2}}{m^{2} n^{2}} \cdot \frac{m n}{1}$

Step 1

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

$\frac{(m + n) (m - n)}{m^{2} n^{2}} \cdot \frac{m n}{1}$

Step 2

Simplify terms.

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Step 2.1

Combine.

$\frac{(m + n) (m - n) (m n)}{m^{2} n^{2} \cdot 1}$

Step 2.2

Cancel the common factor of $m$ and $m^{2}$ .

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Step 2.2.1

Factor $m$ out of $(m + n) (m - n) (m n)$ .

$\frac{m ((m + n) (m - n) (n))}{m^{2} n^{2} \cdot 1}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $m$ out of $m^{2} n^{2} \cdot 1$ .

$\frac{m ((m + n) (m - n) (n))}{m (m n^{2} \cdot 1)}$

Step 2.2.2.2

Cancel the common factor.

$\frac{m ((m + n) (m - n) (n))}{m (m n^{2} \cdot 1)}$

Step 2.2.2.3

Rewrite the expression.

$\frac{(m + n) (m - n) (n)}{m n^{2} \cdot 1}$

Step 2.3

Cancel the common factor of $n$ and $n^{2}$ .

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Step 2.3.1

Factor $n$ out of $(m + n) (m - n) (n)$ .

$\frac{n ((m + n) (m - n))}{m n^{2} \cdot 1}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $n$ out of $m n^{2} \cdot 1$ .

$\frac{n ((m + n) (m - n))}{n (m n \cdot 1)}$

Step 2.3.2.2

Cancel the common factor.

$\frac{n ((m + n) (m - n))}{n (m n \cdot 1)}$

Step 2.3.2.3

Rewrite the expression.

$\frac{(m + n) (m - n)}{m n \cdot 1}$

Step 2.4

Multiply $m$ by $1$ .

$\frac{(m + n) (m - n)}{m n}$