Trigonometry Examples

$0.06 a^{2} - 0.01 a b - 0.12 b^{2}$

Step 1

Factor $0.01$ out of $0.06 a^{2} - 0.01 a b - 0.12 b^{2}$ .

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Step 1.1

Factor $0.01$ out of $0.06 a^{2}$ .

$0.01 (6 a^{2}) - 0.01 a b - 0.12 b^{2}$

Step 1.2

Factor $0.01$ out of $- 0.01 a b$ .

$0.01 (6 a^{2}) + 0.01 (- a b) - 0.12 b^{2}$

Step 1.3

Factor $0.01$ out of $- 0.12 b^{2}$ .

$0.01 (6 a^{2}) + 0.01 (- a b) + 0.01 (- 12 b^{2})$

Step 1.4

Factor $0.01$ out of $0.01 (6 a^{2}) + 0.01 (- a b)$ .

$0.01 (6 a^{2} - a b) + 0.01 (- 12 b^{2})$

Step 1.5

Factor $0.01$ out of $0.01 (6 a^{2} - a b) + 0.01 (- 12 b^{2})$ .

$0.01 (6 a^{2} - a b - 12 b^{2})$

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 $a \cdot c = 6 \cdot - 12 = - 72$ and whose sum is $b = - 1$ .

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Step 2.1.1.1

Reorder terms.

$0.01 (6 a^{2} - 12 b^{2} - a b)$

Step 2.1.1.2

Reorder $- 12 b^{2}$ and $- a b$ .

$0.01 (6 a^{2} - a b - 12 b^{2})$

Step 2.1.1.3

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

$0.01 (6 a^{2} - (a b) - 12 b^{2})$

Step 2.1.1.4

Rewrite $- 1$ as $8$ plus $- 9$

$0.01 (6 a^{2} + (8 - 9) (a b) - 12 b^{2})$

Step 2.1.1.5

Apply the distributive property.

$0.01 (6 a^{2} + 8 (a b) - 9 (a b) - 12 b^{2})$

Step 2.1.1.6

Remove unnecessary parentheses.

$0.01 (6 a^{2} + 8 a b - 9 (a b) - 12 b^{2})$

Step 2.1.1.7

Remove unnecessary parentheses.

$0.01 (6 a^{2} + 8 a b - 9 a b - 12 b^{2})$

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.

$0.01 ((6 a^{2} + 8 a b) - 9 a b - 12 b^{2})$

Step 2.1.2.2

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

$0.01 (2 a (3 a + 4 b) - 3 b (3 a + 4 b))$

Step 2.1.3

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

$0.01 ((3 a + 4 b) (2 a - 3 b))$

Step 2.2

Remove unnecessary parentheses.

$0.01 (3 a + 4 b) (2 a - 3 b)$