Basic Math Examples

$\frac{1}{16} - z^{4}$

Step 1

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

$\frac{1^{2}}{16} - z^{4}$

Step 2

Rewrite $16$ as $4^{2}$ .

$\frac{1^{2}}{4^{2}} - z^{4}$

Step 3

Rewrite $\frac{1^{2}}{4^{2}}$ as ${(\frac{1}{4})}^{2}$ .

${(\frac{1}{4})}^{2} - z^{4}$

Step 4

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

${(\frac{1}{4})}^{2} - {(z^{2})}^{2}$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{1}{4}$ and $b = z^{2}$ .

$(\frac{1}{4} + z^{2}) (\frac{1}{4} - z^{2})$

Step 6

Simplify.

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Step 6.1

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

$(\frac{1}{4} + z^{2}) (\frac{1^{2}}{4} - z^{2})$

Step 6.2

Rewrite $4$ as $2^{2}$ .

$(\frac{1}{4} + z^{2}) (\frac{1^{2}}{2^{2}} - z^{2})$

Step 6.3

Rewrite $\frac{1^{2}}{2^{2}}$ as ${(\frac{1}{2})}^{2}$ .

$(\frac{1}{4} + z^{2}) ({(\frac{1}{2})}^{2} - z^{2})$

Step 6.4

Factor.

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Step 6.4.1

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

$(\frac{1}{4} + z^{2}) ((\frac{1}{2} + z) (\frac{1}{2} - z))$

Step 6.4.2

Remove unnecessary parentheses.

$(\frac{1}{4} + z^{2}) (\frac{1}{2} + z) (\frac{1}{2} - z)$