Algebra Examples

$- 6 x^{4} y - 9 x^{3} y^{2} + 3 x^{2} y^{3}$

Step 1

Factor $- 3 x^{2} y$ out of $- 6 x^{4} y - 9 x^{3} y^{2} + 3 x^{2} y^{3}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $- 6 x^{4} y$ .

$- 9 x^{3} y^{2} + 3 x^{2} y^{3} - 6 x^{4} y$

Step 1.1.2

Reorder $- 9 x^{3} y^{2}$ and $3 x^{2} y^{3}$ .

$3 x^{2} y^{3} - 9 x^{3} y^{2} - 6 x^{4} y$

Step 1.2

Factor $- 3 x^{2} y$ out of $3 x^{2} y^{3}$ .

$- 3 x^{2} y (- 1 y^{2}) - 9 x^{3} y^{2} - 6 x^{4} y$

Step 1.3

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

$- 3 x^{2} y (- 1 y^{2}) - 3 x^{2} y (3 x y) - 6 x^{4} y$

Step 1.4

Factor $- 3 x^{2} y$ out of $- 6 x^{4} y$ .

$- 3 x^{2} y (- 1 y^{2}) - 3 x^{2} y (3 x y) - 3 x^{2} y (2 x^{2})$

Step 1.5

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

$- 3 x^{2} y (- 1 y^{2} + 3 x y) - 3 x^{2} y (2 x^{2})$

Step 1.6

Factor $- 3 x^{2} y$ out of $- 3 x^{2} y (- 1 y^{2} + 3 x y) - 3 x^{2} y (2 x^{2})$ .

$- 3 x^{2} y (- 1 y^{2} + 3 x y + 2 x^{2})$

Step 2

Rewrite $- 1 y^{2}$ as $- y^{2}$ .

$- 3 x^{2} y (- y^{2} + 3 x y + 2 x^{2})$

Step 3

Factor.

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Step 3.1

Factor $- 1$ out of $- y^{2} + 3 x y + 2 x^{2}$ .

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Step 3.1.1

Reorder the expression.

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Step 3.1.1.1

Move $- y^{2}$ .

$- 3 x^{2} y (3 x y + 2 x^{2} - y^{2})$

Step 3.1.1.2

Reorder $3 x y$ and $2 x^{2}$ .

$- 3 x^{2} y (2 x^{2} + 3 x y - y^{2})$

Step 3.1.2

Factor $- 1$ out of $2 x^{2}$ .

$- 3 x^{2} y (- (- 2 x^{2}) + 3 x y - y^{2})$

Step 3.1.3

Factor $- 1$ out of $3 x y$ .

$- 3 x^{2} y (- (- 2 x^{2}) - (- 3 x y) - y^{2})$

Step 3.1.4

Factor $- 1$ out of $- y^{2}$ .

$- 3 x^{2} y (- (- 2 x^{2}) - (- 3 x y) - (y^{2}))$

Step 3.1.5

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

$- 3 x^{2} y (- (- 2 x^{2} - 3 x y) - (y^{2}))$

Step 3.1.6

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

$- 3 x^{2} y (- (- 2 x^{2} - 3 x y + y^{2}))$

Step 3.2

Remove unnecessary parentheses.

$- 3 x^{2} y \cdot - 1 (- 2 x^{2} - 3 x y + y^{2})$

Step 4

Combine exponents.

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Step 4.1

Factor out negative.

$- (- 3 x^{2} y (- 2 x^{2} - 3 x y + y^{2}))$

Step 4.2

Multiply $- 3$ by $- 1$ .

$3 (x^{2} y (- 2 x^{2} - 3 x y + y^{2}))$

Step 5

Remove unnecessary parentheses.

$3 x^{2} y (- 2 x^{2} - 3 x y + y^{2})$

Step 6

Factor.

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Step 6.1

Factor $- 1$ out of $- 2 x^{2} - 3 x y + y^{2}$ .

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Step 6.1.1

Factor $- 1$ out of $- 2 x^{2}$ .

$3 x^{2} y (- (2 x^{2}) - 3 x y + y^{2})$

Step 6.1.2

Factor $- 1$ out of $- 3 x y$ .

$3 x^{2} y (- (2 x^{2}) - (3 x y) + y^{2})$

Step 6.1.3

Factor $- 1$ out of $y^{2}$ .

$3 x^{2} y (- (2 x^{2}) - (3 x y) - 1 (- y^{2}))$

Step 6.1.4

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

$3 x^{2} y (- (2 x^{2} + 3 x y) - 1 (- y^{2}))$

Step 6.1.5

Factor $- 1$ out of $- (2 x^{2} + 3 x y) - 1 (- y^{2})$ .

$3 x^{2} y (- (2 x^{2} + 3 x y - y^{2}))$

Step 6.2

Remove unnecessary parentheses.

$3 x^{2} y \cdot - 1 (2 x^{2} + 3 x y - y^{2})$

Step 7

Combine exponents.

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Step 7.1

Factor out negative.

$- (3 x^{2} y (2 x^{2} + 3 x y - y^{2}))$

Step 7.2

Multiply $3$ by $- 1$ .

$- 3 (x^{2} y (2 x^{2} + 3 x y - y^{2}))$

Step 8

Remove unnecessary parentheses.

$- 3 x^{2} y (2 x^{2} + 3 x y - y^{2})$