Basic Math Examples

$6 a - 2 b^{2} - a + (b - 3 + 9 a^{2})$

Step 1

Remove parentheses.

$6 a - 2 b^{2} - a + b - 3 + 9 a^{2}$

Step 2

Regroup terms.

$- a + b + 6 a - 2 b^{2} - 3 + 9 a^{2}$

Step 3

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

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Step 3.1

Factor $- 1$ out of $- a$ .

$- (a) + b + 6 a - 2 b^{2} - 3 + 9 a^{2}$

Step 3.2

Factor $- 1$ out of $b$ .

$- (a) - 1 (- b) + 6 a - 2 b^{2} - 3 + 9 a^{2}$

Step 3.3

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

$- (a - b) + 6 a - 2 b^{2} - 3 + 9 a^{2}$

Step 4

Regroup terms.

$- (a - b) - 3 + 6 a - 2 b^{2} + 9 a^{2}$

Step 5

Factor $- 1$ out of $6 a - 2 b^{2} + 9 a^{2}$ .

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Step 5.1

Reorder the expression.

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Step 5.1.1

Move $6 a$ .

$- (a - b) - 3 - 2 b^{2} + 9 a^{2} + 6 a$

Step 5.1.2

Reorder $- 2 b^{2}$ and $9 a^{2}$ .

$- (a - b) - 3 + 9 a^{2} - 2 b^{2} + 6 a$

Step 5.2

Factor $- 1$ out of $9 a^{2}$ .

$- (a - b) - 3 - (- 9 a^{2}) - 2 b^{2} + 6 a$

Step 5.3

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

$- (a - b) - 3 - (- 9 a^{2}) - (2 b^{2}) + 6 a$

Step 5.4

Factor $- 1$ out of $6 a$ .

$- (a - b) - 3 - (- 9 a^{2}) - (2 b^{2}) - (- 6 a)$

Step 5.5

Factor $- 1$ out of $- (- 9 a^{2}) - (2 b^{2})$ .

$- (a - b) - 3 - (- 9 a^{2} + 2 b^{2}) - (- 6 a)$

Step 5.6

Factor $- 1$ out of $- (- 9 a^{2} + 2 b^{2}) - (- 6 a)$ .

$- (a - b) - 3 - (- 9 a^{2} + 2 b^{2} - 6 a)$

Step 6

Factor $- 1$ out of $- 3 - (- 9 a^{2} + 2 b^{2} - 6 a)$ .

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Step 6.1

Reorder $- 3$ and $- (- 9 a^{2} + 2 b^{2} - 6 a)$ .

$- (a - b) - (- 9 a^{2} + 2 b^{2} - 6 a) - 3$

Step 6.2

Rewrite $- 3$ as $- 1 (3)$ .

$- (a - b) - (- 9 a^{2} + 2 b^{2} - 6 a) - 1 (3)$

Step 6.3

Factor $- 1$ out of $- (- 9 a^{2} + 2 b^{2} - 6 a) - 1 (3)$ .

$- (a - b) - (- 9 a^{2} + 2 b^{2} - 6 a + 3)$

Step 7

Factor $- 1$ out of $- (a - b) - (- 9 a^{2} + 2 b^{2} - 6 a + 3)$ .

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Step 7.1

Reorder $- (a - b)$ and $- (- 9 a^{2} + 2 b^{2} - 6 a + 3)$ .

$- (- 9 a^{2} + 2 b^{2} - 6 a + 3) - (a - b)$

Step 7.2

Factor $- 1$ out of $- (- 9 a^{2} + 2 b^{2} - 6 a + 3) - (a - b)$ .

$- (- 9 a^{2} + 2 b^{2} - 6 a + 3 + a - b)$

Step 8

Add $- 6 a$ and $a$ .

$- (- 9 a^{2} + 2 b^{2} - 5 a + 3 - b)$