Basic Math Examples

$\frac{25}{36} w^{11} - \frac{49}{100} \cdot (w z^{4})$

Step 1

Remove parentheses.

$\frac{25}{36} w^{11} - \frac{49}{100} \cdot w z^{4}$

Step 2

Factor $w$ out of $\frac{25}{36} w^{11} - \frac{49}{100} \cdot w z^{4}$ .

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Step 2.1

Factor $w$ out of $\frac{25}{36} w^{11}$ .

$w (\frac{25}{36} w^{10}) - \frac{49}{100} \cdot w z^{4}$

Step 2.2

Factor $w$ out of $- \frac{49}{100} \cdot w z^{4}$ .

$w (\frac{25}{36} w^{10}) + w (- \frac{49}{100} z^{4})$

Step 2.3

Factor $w$ out of $w (\frac{25}{36} w^{10}) + w (- \frac{49}{100} z^{4})$ .

$w (\frac{25}{36} w^{10} - \frac{49}{100} z^{4})$

Step 3

Rewrite $\frac{25}{36} w^{10}$ as ${(\frac{5}{6} w^{5})}^{2}$ .

$w ({(\frac{5}{6} w^{5})}^{2} - \frac{49}{100} z^{4})$

Step 4

Rewrite $\frac{49}{100} z^{4}$ as ${(\frac{7}{10} z^{2})}^{2}$ .

$w ({(\frac{5}{6} w^{5})}^{2} - {(\frac{7}{10} z^{2})}^{2})$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{5}{6} w^{5}$ and $b = \frac{7}{10} z^{2}$ .

$w ((\frac{5}{6} w^{5} + \frac{7}{10} z^{2}) (\frac{5}{6} w^{5} - (\frac{7}{10} z^{2})))$

Step 6

Factor.

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Step 6.1

Simplify.

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Step 6.1.1

Combine $\frac{5}{6}$ and $w^{5}$ .

$w ((\frac{5 w^{5}}{6} + \frac{7}{10} z^{2}) (\frac{5}{6} w^{5} - (\frac{7}{10} z^{2})))$

Step 6.1.2

Combine $\frac{7}{10}$ and $z^{2}$ .

$w ((\frac{5 w^{5}}{6} + \frac{7 z^{2}}{10}) (\frac{5}{6} w^{5} - (\frac{7}{10} z^{2})))$

Step 6.1.3

Combine $\frac{5}{6}$ and $w^{5}$ .

$w ((\frac{5 w^{5}}{6} + \frac{7 z^{2}}{10}) (\frac{5 w^{5}}{6} - (\frac{7}{10} z^{2})))$

Step 6.1.4

Combine $\frac{7}{10}$ and $z^{2}$ .

$w ((\frac{5 w^{5}}{6} + \frac{7 z^{2}}{10}) (\frac{5 w^{5}}{6} - \frac{7 z^{2}}{10}))$

Step 6.2

Remove unnecessary parentheses.

$w (\frac{5 w^{5}}{6} + \frac{7 z^{2}}{10}) (\frac{5 w^{5}}{6} - \frac{7 z^{2}}{10})$