Algebra Examples

$\frac{30 c^{8} d^{3} - 36 c^{6} d^{2} + 6 c^{3} d}{12 c^{2} d}$

Step 1

Factor $6 c^{3} d$ out of $30 c^{8} d^{3} - 36 c^{6} d^{2} + 6 c^{3} d$ .

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Step 1.1

Factor $6 c^{3} d$ out of $30 c^{8} d^{3}$ .

$\frac{6 c^{3} d (5 c^{5} d^{2}) - 36 c^{6} d^{2} + 6 c^{3} d}{12 c^{2} d}$

Step 1.2

Factor $6 c^{3} d$ out of $- 36 c^{6} d^{2}$ .

$\frac{6 c^{3} d (5 c^{5} d^{2}) + 6 c^{3} d (- 6 c^{3} d) + 6 c^{3} d}{12 c^{2} d}$

Step 1.3

Factor $6 c^{3} d$ out of $6 c^{3} d$ .

$\frac{6 c^{3} d (5 c^{5} d^{2}) + 6 c^{3} d (- 6 c^{3} d) + 6 c^{3} d (1)}{12 c^{2} d}$

Step 1.4

Factor $6 c^{3} d$ out of $6 c^{3} d (5 c^{5} d^{2}) + 6 c^{3} d (- 6 c^{3} d)$ .

$\frac{6 c^{3} d (5 c^{5} d^{2} - 6 c^{3} d) + 6 c^{3} d (1)}{12 c^{2} d}$

Step 1.5

Factor $6 c^{3} d$ out of $6 c^{3} d (5 c^{5} d^{2} - 6 c^{3} d) + 6 c^{3} d (1)$ .

$\frac{6 c^{3} d (5 c^{5} d^{2} - 6 c^{3} d + 1)}{12 c^{2} d}$

Step 2

Cancel the common factor of $6$ and $12$ .

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Step 2.1

Factor $6$ out of $6 c^{3} d (5 c^{5} d^{2} - 6 c^{3} d + 1)$ .

$\frac{6 (c^{3} d (5 c^{5} d^{2} - 6 c^{3} d + 1))}{12 c^{2} d}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $6$ out of $12 c^{2} d$ .

$\frac{6 (c^{3} d (5 c^{5} d^{2} - 6 c^{3} d + 1))}{6 (2 c^{2} d)}$

Step 2.2.2

Cancel the common factor.

$\frac{6 (c^{3} d (5 c^{5} d^{2} - 6 c^{3} d + 1))}{6 (2 c^{2} d)}$

Step 2.2.3

Rewrite the expression.

$\frac{c^{3} d (5 c^{5} d^{2} - 6 c^{3} d + 1)}{2 c^{2} d}$

Step 3

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

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Step 3.1

Factor $c^{2}$ out of $c^{3} d (5 c^{5} d^{2} - 6 c^{3} d + 1)$ .

$\frac{c^{2} (c d (5 c^{5} d^{2} - 6 c^{3} d + 1))}{2 c^{2} d}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $c^{2}$ out of $2 c^{2} d$ .

$\frac{c^{2} (c d (5 c^{5} d^{2} - 6 c^{3} d + 1))}{c^{2} (2 d)}$

Step 3.2.2

Cancel the common factor.

$\frac{c^{2} (c d (5 c^{5} d^{2} - 6 c^{3} d + 1))}{c^{2} (2 d)}$

Step 3.2.3

Rewrite the expression.

$\frac{c d (5 c^{5} d^{2} - 6 c^{3} d + 1)}{2 d}$

Step 4

Cancel the common factor of $d$ .

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Step 4.1

Cancel the common factor.

$\frac{c d (5 c^{5} d^{2} - 6 c^{3} d + 1)}{2 d}$

Step 4.2

Rewrite the expression.

$\frac{c (5 c^{5} d^{2} - 6 c^{3} d + 1)}{2}$