Calculus Examples

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

Step 1

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

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

Step 2

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 $b = z$ .

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

Step 3

Reorder terms.

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

Step 4

Factor.

Tap for more steps...

Step 4.1

Factor $- 1$ out of $- z^{2} + z + 1$ .

Tap for more steps...

Step 4.1.1

Factor $- 1$ out of $- z^{2}$ .

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

Step 4.1.2

Factor $- 1$ out of $z$ .

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

Step 4.1.3

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 4.1.4

Factor $- 1$ out of $- (z^{2}) - 1 (- z)$ .

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

Step 4.1.5

Factor $- 1$ out of $- (z^{2} - z) - 1 (- 1)$ .

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

Step 4.2

Remove unnecessary parentheses.

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

Step 5

Factor out negative.

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

Step 6

Remove unnecessary parentheses.

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