Basic Math Examples

$6 v^{2} - 72 v^{3} + 2 v y - v$

Step 1

Factor $v$ out of $6 v^{2} - 72 v^{3} + 2 v y - v$ .

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Step 1.1

Factor $v$ out of $6 v^{2}$ .

$v (6 v) - 72 v^{3} + 2 v y - v$

Step 1.2

Factor $v$ out of $- 72 v^{3}$ .

$v (6 v) + v (- 72 v^{2}) + 2 v y - v$

Step 1.3

Factor $v$ out of $2 v y$ .

$v (6 v) + v (- 72 v^{2}) + v (2 y) - v$

Step 1.4

Factor $v$ out of $- v$ .

$v (6 v) + v (- 72 v^{2}) + v (2 y) + v \cdot - 1$

Step 1.5

Factor $v$ out of $v (6 v) + v (- 72 v^{2})$ .

$v (6 v - 72 v^{2}) + v (2 y) + v \cdot - 1$

Step 1.6

Factor $v$ out of $v (6 v - 72 v^{2}) + v (2 y)$ .

$v (6 v - 72 v^{2} + 2 y) + v \cdot - 1$

Step 1.7

Factor $v$ out of $v (6 v - 72 v^{2} + 2 y) + v \cdot - 1$ .

$v (6 v - 72 v^{2} + 2 y - 1)$

Step 2

Regroup terms.

$v (- 1 + 6 v - 72 v^{2} + 2 y)$

Step 3

Factor $- 2$ out of $6 v - 72 v^{2} + 2 y$ .

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Step 3.1

Move $6 v$ .

$v (- 1 - 72 v^{2} + 2 y + 6 v)$

Step 3.2

Factor $- 2$ out of $- 72 v^{2}$ .

$v (- 1 - 2 (36 v^{2}) + 2 y + 6 v)$

Step 3.3

Factor $- 2$ out of $2 y$ .

$v (- 1 - 2 (36 v^{2}) - 2 (- y) + 6 v)$

Step 3.4

Factor $- 2$ out of $6 v$ .

$v (- 1 - 2 (36 v^{2}) - 2 (- y) - 2 (- 3 v))$

Step 3.5

Factor $- 2$ out of $- 2 (36 v^{2}) - 2 (- y)$ .

$v (- 1 - 2 (36 v^{2} - y) - 2 (- 3 v))$

Step 3.6

Factor $- 2$ out of $- 2 (36 v^{2} - y) - 2 (- 3 v)$ .

$v (- 1 - 2 (36 v^{2} - y - 3 v))$

Step 4

Factor $- 1$ out of $- 1 - 2 (36 v^{2} - y - 3 v)$ .

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Step 4.1

Reorder $- 1$ and $- 2 (36 v^{2} - y - 3 v)$ .

$v (- 2 (36 v^{2} - y - 3 v) - 1)$

Step 4.2

Factor $- 1$ out of $- 2 (36 v^{2} - y - 3 v)$ .

$v (- (2 (36 v^{2} - y - 3 v)) - 1)$

Step 4.3

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

$v (- (2 (36 v^{2} - y - 3 v)) - 1 (1))$

Step 4.4

Factor $- 1$ out of $- (2 (36 v^{2} - y - 3 v)) - 1 (1)$ .

$v (- (2 (36 v^{2} - y - 3 v) + 1))$

Step 5

Apply the distributive property.

$v (- (2 (36 v^{2}) + 2 (- y) + 2 (- 3 v) + 1))$

Step 6

Factor.

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Step 6.1

Simplify.

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Step 6.1.1

Multiply $36$ by $2$ .

$v (- (72 v^{2} + 2 (- y) + 2 (- 3 v) + 1))$

Step 6.1.2

Multiply $- 1$ by $2$ .

$v (- (72 v^{2} - 2 y + 2 (- 3 v) + 1))$

Step 6.1.3

Multiply $- 3$ by $2$ .

$v (- (72 v^{2} - 2 y - 6 v + 1))$

Step 6.2

Remove unnecessary parentheses.

$v \cdot - 1 (72 v^{2} - 2 y - 6 v + 1)$

Step 7

Factor out negative.

$- (v (72 v^{2} - 2 y - 6 v + 1))$

Step 8

Remove unnecessary parentheses.

$- v (72 v^{2} - 2 y - 6 v + 1)$