Basic Math Examples

$z \cdot (9 z) - 9$

Step 1

Factor $9$ out of $z \cdot (9 z) - 9$ .

Tap for more steps...

Step 1.1

Factor $9$ out of $z \cdot (9 z)$ .

$9 (z \cdot (z)) - 9$

Step 1.2

Factor $9$ out of $- 9$ .

$9 (z \cdot (z)) + 9 (- 1)$

Step 1.3

Factor $9$ out of $9 (z \cdot (z)) + 9 (- 1)$ .

$9 (z \cdot (z) - 1)$

Step 2

Raise $z$ to the power of $1$ .

$9 (z^{1} \cdot z - 1)$

Step 3

Raise $z$ to the power of $1$ .

$9 (z^{1} \cdot z^{1} - 1)$

Step 4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$9 (z^{1 + 1} - 1)$

Step 5

Add $1$ and $1$ .

$9 (z^{2} - 1)$

Step 6

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

$9 (z^{2} - 1^{2})$

Step 7

Factor.

Tap for more steps...

Step 7.1

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

$9 ((z + 1) (z - 1))$

Step 7.2

Remove unnecessary parentheses.

$9 (z + 1) (z - 1)$