Algebra Examples

$\frac{(8 c d^{3}) (- 3 c^{4})}{6 c^{2} d} - 9 c^{3} d^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $c$ by $c^{4}$ by adding the exponents.

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Step 1.1.1

Move $c^{4}$ .

$\frac{8 (c^{4} c) d^{3} \cdot - 3}{6 c^{2} d} - 9 c^{3} d^{2}$

Step 1.1.2

Multiply $c^{4}$ by $c$ .

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Step 1.1.2.1

Raise $c$ to the power of $1$ .

$\frac{8 (c^{4} c^{1}) d^{3} \cdot - 3}{6 c^{2} d} - 9 c^{3} d^{2}$

Step 1.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{8 c^{4 + 1} d^{3} \cdot - 3}{6 c^{2} d} - 9 c^{3} d^{2}$

Step 1.1.3

Add $4$ and $1$ .

$\frac{8 c^{5} d^{3} \cdot - 3}{6 c^{2} d} - 9 c^{3} d^{2}$

Step 1.2

Cancel the common factor of $8$ and $6$ .

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Step 1.2.1

Factor $2$ out of $8 c^{5} d^{3} \cdot - 3$ .

$\frac{2 (4 c^{5} d^{3} \cdot - 3)}{6 c^{2} d} - 9 c^{3} d^{2}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

$\frac{2 (4 c^{5} d^{3} \cdot - 3)}{2 (3 c^{2} d)} - 9 c^{3} d^{2}$

Step 1.2.2.2

Cancel the common factor.

$\frac{2 (4 c^{5} d^{3} \cdot - 3)}{2 (3 c^{2} d)} - 9 c^{3} d^{2}$

Step 1.2.2.3

Rewrite the expression.

$\frac{4 c^{5} d^{3} \cdot - 3}{3 c^{2} d} - 9 c^{3} d^{2}$

Step 1.3

Cancel the common factor of $c^{5}$ and $c^{2}$ .

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Step 1.3.1

Factor $c^{2}$ out of $4 c^{5} d^{3} \cdot - 3$ .

$\frac{c^{2} (4 c^{3} d^{3} \cdot - 3)}{3 c^{2} d} - 9 c^{3} d^{2}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

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

$\frac{c^{2} (4 c^{3} d^{3} \cdot - 3)}{c^{2} (3 d)} - 9 c^{3} d^{2}$

Step 1.3.2.2

Cancel the common factor.

$\frac{c^{2} (4 c^{3} d^{3} \cdot - 3)}{c^{2} (3 d)} - 9 c^{3} d^{2}$

Step 1.3.2.3

Rewrite the expression.

$\frac{4 c^{3} d^{3} \cdot - 3}{3 d} - 9 c^{3} d^{2}$

Step 1.4

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

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Step 1.4.1

Factor $d$ out of $4 c^{3} d^{3} \cdot - 3$ .

$\frac{d (4 c^{3} d^{2} \cdot - 3)}{3 d} - 9 c^{3} d^{2}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $d$ out of $3 d$ .

$\frac{d (4 c^{3} d^{2} \cdot - 3)}{d \cdot 3} - 9 c^{3} d^{2}$

Step 1.4.2.2

Cancel the common factor.

$\frac{d (4 c^{3} d^{2} \cdot - 3)}{d \cdot 3} - 9 c^{3} d^{2}$

Step 1.4.2.3

Rewrite the expression.

$\frac{4 c^{3} d^{2} \cdot - 3}{3} - 9 c^{3} d^{2}$

Step 1.5

Cancel the common factor of $- 3$ and $3$ .

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Step 1.5.1

Factor $3$ out of $4 c^{3} d^{2} \cdot - 3$ .

$\frac{3 (4 c^{3} d^{2} \cdot - 1)}{3} - 9 c^{3} d^{2}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $3$ out of $3$ .

$\frac{3 (4 c^{3} d^{2} \cdot - 1)}{3 (1)} - 9 c^{3} d^{2}$

Step 1.5.2.2

Cancel the common factor.

$\frac{3 (4 c^{3} d^{2} \cdot - 1)}{3 \cdot 1} - 9 c^{3} d^{2}$

Step 1.5.2.3

Rewrite the expression.

$\frac{4 c^{3} d^{2} \cdot - 1}{1} - 9 c^{3} d^{2}$

Step 1.5.2.4

Divide $4 c^{3} d^{2} \cdot - 1$ by $1$ .

$4 c^{3} d^{2} \cdot - 1 - 9 c^{3} d^{2}$

Step 1.6

Multiply $- 1$ by $4$ .

$- 4 c^{3} d^{2} - 9 c^{3} d^{2}$

Step 2

Subtract $9 c^{3} d^{2}$ from $- 4 c^{3} d^{2}$ .

$- 13 c^{3} d^{2}$