Calculus Examples

$8 a^{2} - 2 a b - 6 b^{2}$

Step 1

Factor $2$ out of $8 a^{2} - 2 a b - 6 b^{2}$ .

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Step 1.1

Factor $2$ out of $8 a^{2}$ .

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

Step 1.2

Factor $2$ out of $- 2 a b$ .

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

Step 1.3

Factor $2$ out of $- 6 b^{2}$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 3 = - 12$ and whose sum is $b = - 1$ .

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Step 2.1.1.1

Reorder terms.

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

Step 2.1.1.2

Reorder $- 3 b^{2}$ and $- a b$ .

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

Step 2.1.1.3

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

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

Step 2.1.1.4

Rewrite $- 1$ as $3$ plus $- 4$

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

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Remove unnecessary parentheses.

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

Step 2.1.1.7

Remove unnecessary parentheses.

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

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

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

Step 2.1.2.2

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

$2 (a (4 a + 3 b) - b (4 a + 3 b))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $4 a + 3 b$ .

$2 ((4 a + 3 b) (a - b))$

Step 2.2

Remove unnecessary parentheses.

$2 (4 a + 3 b) (a - b)$