Algebra Examples

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

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

Step 1

Factor

- 3 x^{2} y

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

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

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

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move

- 6 x^{4} y

$- 6 x^{4} y$ .

- 9 x^{3} y^{2} + 3 x^{2} y^{3} - 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}

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

3 x^{2} y^{3}

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

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

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

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

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

Step 1.2

Factor

- 3 x^{2} y

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

3 x^{2} y^{3}

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

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

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

Step 1.3

Factor

- 3 x^{2} y

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

- 9 x^{3} y^{2}

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

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

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

Step 1.4

Factor

- 3 x^{2} y

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

- 6 x^{4} y

$- 6 x^{4} y$ .

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

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

Step 1.5

Factor

- 3 x^{2} y

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

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

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

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

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

Step 1.6

Factor

- 3 x^{2} y

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

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

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

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

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

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

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

Step 2

Rewrite

- 1 y^{2}

$- 1 y^{2}$ as

- y^{2}

$- y^{2}$ .

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

$- 1$ out of

- y^{2} + 3 x y + 2 x^{2}

$- y^{2} + 3 x y + 2 x^{2}$ .

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Step 3.1.1

Reorder the expression.

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Step 3.1.1.1

Move

- y^{2}

$- y^{2}$ .

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

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

Step 3.1.1.2

Reorder

3 x y

$3 x y$ and

2 x^{2}

$2 x^{2}$ .

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

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

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

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

Step 3.1.2

Factor

- 1

$- 1$ out of

2 x^{2}

$2 x^{2}$ .

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

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

Step 3.1.3

Factor

- 1

$- 1$ out of

3 x y

$3 x y$ .

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

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

Step 3.1.4

Factor

- 1

$- 1$ out of

- y^{2}

$- y^{2}$ .

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

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

Step 3.1.5

Factor

- 1

$- 1$ out of

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

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

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

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

Step 3.1.6

Factor

- 1

$- 1$ out of

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

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

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

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

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

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

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

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

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}))

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

Step 4.2

Multiply

- 3

$- 3$ by

- 1

$- 1$ .

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

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

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

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

Step 5

Remove unnecessary parentheses.

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

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

Step 6

Factor.

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Step 6.1

Factor

- 1

$- 1$ out of

- 2 x^{2} - 3 x y + y^{2}

$- 2 x^{2} - 3 x y + y^{2}$ .

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Step 6.1.1

Factor

- 1

$- 1$ out of

- 2 x^{2}

$- 2 x^{2}$ .

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

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

Step 6.1.2

Factor

- 1

$- 1$ out of

- 3 x y

$- 3 x y$ .

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

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

Step 6.1.3

Factor

- 1

$- 1$ out of

y^{2}

$y^{2}$ .

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

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

Step 6.1.4

Factor

- 1

$- 1$ out of

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

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

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

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

Step 6.1.5

Factor

- 1

$- 1$ out of

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

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

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

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

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

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

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

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

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}))

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

Step 7.2

Multiply

3

$3$ by

- 1

$- 1$ .

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

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

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

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

Step 8

Remove unnecessary parentheses.

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

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