Algebra Examples

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

Step 1

Regroup terms.

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

Step 2

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

Tap for more steps...

Step 2.1

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

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

Step 2.2

Factor $- 1$ out of $- n$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $b$ by $1$ .

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

Step 5

Factor.

Tap for more steps...

Step 5.1

Rewrite $b n + b + n + 1$ in a factored form.

Tap for more steps...

Step 5.1.1

Factor out the greatest common factor from each group.

Tap for more steps...

Step 5.1.1.1

Group the first two terms and the last two terms.

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

Step 5.1.1.2

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

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

Step 5.1.2

Factor the polynomial by factoring out the greatest common factor, $n + 1$ .

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

Step 5.2

Remove unnecessary parentheses.

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

Step 6

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

Tap for more steps...

Step 6.1

Factor $n + 1$ out of $a (n + 1)$ .

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

Step 6.2

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

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

Step 6.3

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

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

Step 7

Apply the distributive property.

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

Step 8

Rewrite $- 1 b$ as $- b$ .

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

Step 9

Multiply $- 1$ by $1$ .

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