Basic Math Examples

$a^{2} b - a b - a^{2} + a$

Step 1

Factor $a$ out of $a^{2} b - a b - a^{2} + a$ .

Tap for more steps...

Step 1.1

Factor $a$ out of $a^{2} b$ .

$a (a b) - a b - a^{2} + a$

Step 1.2

Factor $a$ out of $- a b$ .

$a (a b) + a (- 1 b) - a^{2} + a$

Step 1.3

Factor $a$ out of $- a^{2}$ .

$a (a b) + a (- 1 b) + a (- a) + a$

Step 1.4

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

$a (a b) + a (- 1 b) + a (- a) + a^{1}$

Step 1.5

Factor $a$ out of $a^{1}$ .

$a (a b) + a (- 1 b) + a (- a) + a \cdot 1$

Step 1.6

Factor $a$ out of $a (a b) + a (- 1 b)$ .

$a (a b - 1 b) + a (- a) + a \cdot 1$

Step 1.7

Factor $a$ out of $a (a b - 1 b) + a (- a)$ .

$a (a b - 1 b - a) + a \cdot 1$

Step 1.8

Factor $a$ out of $a (a b - 1 b - a) + a \cdot 1$ .

$a (a b - 1 b - a + 1)$

Step 2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.1

Group the first two terms and the last two terms.

$a ((a b - 1 b) - a + 1)$

Step 2.2

Factor out the greatest common factor (GCF) from each group.

$a (b (a - 1) - (a - 1))$

Step 3

Factor.

Tap for more steps...

Step 3.1

Factor the polynomial by factoring out the greatest common factor, $a - 1$ .

$a ((a - 1) (b - 1))$

Step 3.2

Remove unnecessary parentheses.

$a (a - 1) (b - 1)$