Algebra Examples

$\frac{16 x^{6} y^{5} z - 12 x^{4} y^{6} z^{2} + 6 x^{3} y^{9}}{- 4 x^{2} y}$

Step 1

Factor $2 x^{3} y^{5}$ out of $16 x^{6} y^{5} z - 12 x^{4} y^{6} z^{2} + 6 x^{3} y^{9}$ .

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Step 1.1

Factor $2 x^{3} y^{5}$ out of $16 x^{6} y^{5} z$ .

$\frac{2 x^{3} y^{5} (8 x^{3} z) - 12 x^{4} y^{6} z^{2} + 6 x^{3} y^{9}}{- 4 x^{2} y}$

Step 1.2

Factor $2 x^{3} y^{5}$ out of $- 12 x^{4} y^{6} z^{2}$ .

$\frac{2 x^{3} y^{5} (8 x^{3} z) + 2 x^{3} y^{5} (- 6 x y z^{2}) + 6 x^{3} y^{9}}{- 4 x^{2} y}$

Step 1.3

Factor $2 x^{3} y^{5}$ out of $6 x^{3} y^{9}$ .

$\frac{2 x^{3} y^{5} (8 x^{3} z) + 2 x^{3} y^{5} (- 6 x y z^{2}) + 2 x^{3} y^{5} (3 y^{4})}{- 4 x^{2} y}$

Step 1.4

Factor $2 x^{3} y^{5}$ out of $2 x^{3} y^{5} (8 x^{3} z) + 2 x^{3} y^{5} (- 6 x y z^{2})$ .

$\frac{2 x^{3} y^{5} (8 x^{3} z - 6 x y z^{2}) + 2 x^{3} y^{5} (3 y^{4})}{- 4 x^{2} y}$

Step 1.5

Factor $2 x^{3} y^{5}$ out of $2 x^{3} y^{5} (8 x^{3} z - 6 x y z^{2}) + 2 x^{3} y^{5} (3 y^{4})$ .

$\frac{2 x^{3} y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})}{- 4 x^{2} y}$

Step 2

Cancel the common factor of $2$ and $- 4$ .

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Step 2.1

Factor $2$ out of $2 x^{3} y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})$ .

$\frac{2 (x^{3} y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{- 4 x^{2} y}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{2 (x^{3} y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{2 (- 2 x^{2} y)}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (x^{3} y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{2 (- 2 x^{2} y)}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{3} y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})}{- 2 x^{2} y}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $x^{3} y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})$ .

$\frac{x^{2} (x y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{- 2 x^{2} y}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{x^{2} (x y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{x^{2} (- 2 y)}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (x y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{x^{2} (- 2 y)}$

Step 3.2.3

Rewrite the expression.

$\frac{x y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})}{- 2 y}$

Step 4

Cancel the common factor of $y^{5}$ and $y$ .

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Step 4.1

Factor $y$ out of $x y^{5} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})$ .

$\frac{y (x y^{4} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{- 2 y}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y$ out of $- 2 y$ .

$\frac{y (x y^{4} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{y \cdot - 2}$

Step 4.2.2

Cancel the common factor.

$\frac{y (x y^{4} (8 x^{3} z - 6 x y z^{2} + 3 y^{4}))}{y \cdot - 2}$

Step 4.2.3

Rewrite the expression.

$\frac{x y^{4} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})}{- 2}$

Step 5

Move the negative in front of the fraction.

$- \frac{x y^{4} (8 x^{3} z - 6 x y z^{2} + 3 y^{4})}{2}$