Algebra Examples

$3 s t^{2} - 9 s^{3} t + 6 s^{2} t^{2}$

Step 1

Factor $- 3 s t$ out of $3 s t^{2} - 9 s^{3} t + 6 s^{2} t^{2}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $3 s t^{2}$ .

$- 9 s^{3} t + 6 s^{2} t^{2} + 3 s t^{2}$

Step 1.1.2

Reorder $- 9 s^{3} t$ and $6 s^{2} t^{2}$ .

$6 s^{2} t^{2} - 9 s^{3} t + 3 s t^{2}$

Step 1.2

Factor $- 3 s t$ out of $6 s^{2} t^{2}$ .

$- 3 s t (- 2 s t) - 9 s^{3} t + 3 s t^{2}$

Step 1.3

Factor $- 3 s t$ out of $- 9 s^{3} t$ .

$- 3 s t (- 2 s t) - 3 s t (3 s^{2}) + 3 s t^{2}$

Step 1.4

Factor $- 3 s t$ out of $3 s t^{2}$ .

$- 3 s t (- 2 s t) - 3 s t (3 s^{2}) - 3 s t (- 1 t)$

Step 1.5

Factor $- 3 s t$ out of $- 3 s t (- 2 s t) - 3 s t (3 s^{2})$ .

$- 3 s t (- 2 s t + 3 s^{2}) - 3 s t (- 1 t)$

Step 1.6

Factor $- 3 s t$ out of $- 3 s t (- 2 s t + 3 s^{2}) - 3 s t (- 1 t)$ .

$- 3 s t (- 2 s t + 3 s^{2} - 1 t)$

Step 2

Rewrite $- 1 t$ as $- t$ .

$- 3 s t (- 2 s t + 3 s^{2} - t)$

Step 3

Factor.

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Step 3.1

Factor $- 1$ out of $- 2 s t + 3 s^{2} - t$ .

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Step 3.1.1

Factor $- 1$ out of $- 2 s t$ .

$- 3 s t (- (2 s t) + 3 s^{2} - t)$

Step 3.1.2

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

$- 3 s t (- (2 s t) - (- 3 s^{2}) - t)$

Step 3.1.3

Factor $- 1$ out of $- t$ .

$- 3 s t (- (2 s t) - (- 3 s^{2}) - (t))$

Step 3.1.4

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

$- 3 s t (- (2 s t - 3 s^{2}) - (t))$

Step 3.1.5

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

$- 3 s t (- (2 s t - 3 s^{2} + t))$

Step 3.2

Remove unnecessary parentheses.

$- 3 s t \cdot - 1 (2 s t - 3 s^{2} + t)$

Step 4

Combine exponents.

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Step 4.1

Factor out negative.

$- (- 3 s t (2 s t - 3 s^{2} + t))$

Step 4.2

Multiply $- 3$ by $- 1$ .

$3 (s t (2 s t - 3 s^{2} + t))$

Step 5

Remove unnecessary parentheses.

$3 s t (2 s t - 3 s^{2} + t)$