Basic Math Examples

$2 a^{2} b + 2 b^{2} - 3 a b - 4 (a b - b^{2})$

Step 1

Group the last three terms.

$2 a^{2} b + 2 b^{2} - 3 a b - 4 (a b - b^{2})$

Step 2

Factor.

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Step 2.1

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

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Step 2.1.1

Factor $b$ out of $a b$ .

$2 a^{2} b + 2 b^{2} - 3 a b - 4 (b a - b^{2})$

Step 2.1.2

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

$2 a^{2} b + 2 b^{2} - 3 a b - 4 (b a + b (- b))$

Step 2.1.3

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

$2 a^{2} b + 2 b^{2} - 3 a b - 4 (b (a - b))$

Step 2.2

Remove unnecessary parentheses.

$2 a^{2} b + 2 b^{2} - 3 a b - 4 b (a - b)$

Step 3

Factor $b$ out of $2 a^{2} b + 2 b^{2} - 3 a b - 4 b (a - b)$ .

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Step 3.1

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

$b (2 a^{2}) + 2 b^{2} - 3 a b - 4 b (a - b)$

Step 3.2

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

$b (2 a^{2}) + b (2 b) - 3 a b - 4 b (a - b)$

Step 3.3

Factor $b$ out of $- 3 a b$ .

$b (2 a^{2}) + b (2 b) + b (- 3 a) - 4 b (a - b)$

Step 3.4

Factor $b$ out of $- 4 b (a - b)$ .

$b (2 a^{2}) + b (2 b) + b (- 3 a) + b (- 4 (a - b))$

Step 3.5

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

$b (2 a^{2} + 2 b) + b (- 3 a) + b (- 4 (a - b))$

Step 3.6

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

$b (2 a^{2} + 2 b - 3 a) + b (- 4 (a - b))$

Step 3.7

Factor $b$ out of $b (2 a^{2} + 2 b - 3 a) + b (- 4 (a - b))$ .

$b (2 a^{2} + 2 b - 3 a - 4 (a - b))$

Step 4

Apply the distributive property.

$b (2 a^{2} + 2 b - 3 a - 4 a - 4 (- b))$

Step 5

Multiply $- 1$ by $- 4$ .

$b (2 a^{2} + 2 b - 3 a - 4 a + 4 b)$

Step 6

Add $2 b$ and $4 b$ .

$b (2 a^{2} - 3 a - 4 a + 6 b)$

Step 7

Subtract $4 a$ from $- 3 a$ .

$b (2 a^{2} - 7 a + 6 b)$