Basic Math Examples

$(- r^{3} - 3 r^{2} + 9 r - 9) \div (r - 1)$

Step 1

Rewrite the division as a fraction.

$\frac{- r^{3} - 3 r^{2} + 9 r - 9}{r - 1}$

Step 2

Factor $- 1$ out of $- r^{3}$ .

$\frac{- (r^{3}) - 3 r^{2} + 9 r - 9}{r - 1}$

Step 3

Factor $- 1$ out of $- 3 r^{2}$ .

$\frac{- (r^{3}) - (3 r^{2}) + 9 r - 9}{r - 1}$

Step 4

Factor $- 1$ out of $- (r^{3}) - (3 r^{2})$ .

$\frac{- (r^{3} + 3 r^{2}) + 9 r - 9}{r - 1}$

Step 5

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

$\frac{- (r^{3} + 3 r^{2}) - (- 9 r) - 9}{r - 1}$

Step 6

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

$\frac{- (r^{3} + 3 r^{2} - 9 r) - 9}{r - 1}$

Step 7

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- (r^{3} + 3 r^{2} - 9 r) - 1 (9)}{r - 1}$

Step 8

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

$\frac{- (r^{3} + 3 r^{2} - 9 r + 9)}{r - 1}$

Step 9

Simplify the expression.

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Step 9.1

Rewrite $- (r^{3} + 3 r^{2} - 9 r + 9)$ as $- 1 (r^{3} + 3 r^{2} - 9 r + 9)$ .

$\frac{- 1 (r^{3} + 3 r^{2} - 9 r + 9)}{r - 1}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{r^{3} + 3 r^{2} - 9 r + 9}{r - 1}$