Algebra Examples

$(- 9 a^{4} - 9 a^{3} - 4 a^{2}) \div 9 a$

Step 1

Rewrite the division as a fraction.

$\frac{- 9 a^{4} - 9 a^{3} - 4 a^{2}}{9 a}$

Step 2

Factor $a^{2}$ out of $- 9 a^{4} - 9 a^{3} - 4 a^{2}$ .

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Step 2.1

Factor $a^{2}$ out of $- 9 a^{4}$ .

$\frac{a^{2} (- 9 a^{2}) - 9 a^{3} - 4 a^{2}}{9 a}$

Step 2.2

Factor $a^{2}$ out of $- 9 a^{3}$ .

$\frac{a^{2} (- 9 a^{2}) + a^{2} (- 9 a) - 4 a^{2}}{9 a}$

Step 2.3

Factor $a^{2}$ out of $- 4 a^{2}$ .

$\frac{a^{2} (- 9 a^{2}) + a^{2} (- 9 a) + a^{2} \cdot - 4}{9 a}$

Step 2.4

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

$\frac{a^{2} (- 9 a^{2} - 9 a) + a^{2} \cdot - 4}{9 a}$

Step 2.5

Factor $a^{2}$ out of $a^{2} (- 9 a^{2} - 9 a) + a^{2} \cdot - 4$ .

$\frac{a^{2} (- 9 a^{2} - 9 a - 4)}{9 a}$

Step 3

Cancel the common factor of $a^{2}$ and $a$ .

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Step 3.1

Factor $a$ out of $a^{2} (- 9 a^{2} - 9 a - 4)$ .

$\frac{a (a (- 9 a^{2} - 9 a - 4))}{9 a}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $9 a$ .

$\frac{a (a (- 9 a^{2} - 9 a - 4))}{a \cdot 9}$

Step 3.2.2

Cancel the common factor.

$\frac{a (a (- 9 a^{2} - 9 a - 4))}{a \cdot 9}$

Step 3.2.3

Rewrite the expression.

$\frac{a (- 9 a^{2} - 9 a - 4)}{9}$

Step 4

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

$\frac{a (- (9 a^{2}) - 9 a - 4)}{9}$

Step 5

Factor $- 1$ out of $- 9 a$ .

$\frac{a (- (9 a^{2}) - (9 a) - 4)}{9}$

Step 6

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

$\frac{a (- (9 a^{2} + 9 a) - 4)}{9}$

Step 7

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{a (- (9 a^{2} + 9 a) - 1 (4))}{9}$

Step 8

Factor $- 1$ out of $- (9 a^{2} + 9 a) - 1 (4)$ .

$\frac{a (- (9 a^{2} + 9 a + 4))}{9}$

Step 9

Simplify the expression.

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Step 9.1

Rewrite $- (9 a^{2} + 9 a + 4)$ as $- 1 (9 a^{2} + 9 a + 4)$ .

$\frac{a (- 1 (9 a^{2} + 9 a + 4))}{9}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{a (9 a^{2} + 9 a + 4)}{9}$