Pre-Algebra Examples

$\frac{- 25 c^{5} - 5 c^{2}}{5 c}$

Step 1

Factor $5 c^{2}$ out of $- 25 c^{5} - 5 c^{2}$ .

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Step 1.1

Factor $5 c^{2}$ out of $- 25 c^{5}$ .

$\frac{5 c^{2} (- 5 c^{3}) - 5 c^{2}}{5 c}$

Step 1.2

Factor $5 c^{2}$ out of $- 5 c^{2}$ .

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

Step 1.3

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

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

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

$\frac{c (c (- 5 c^{3} - 1))}{c}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{c (c (- 5 c^{3} - 1))}{c^{1}}$

Step 3.2.2

Factor $c$ out of $c^{1}$ .

$\frac{c (c (- 5 c^{3} - 1))}{c \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{c (c (- 5 c^{3} - 1))}{c \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{c (- 5 c^{3} - 1)}{1}$

Step 3.2.5

Divide $c (- 5 c^{3} - 1)$ by $1$ .

$c (- 5 c^{3} - 1)$

Step 4

Apply the distributive property.

$c (- 5 c^{3}) + c \cdot - 1$

Step 5

Rewrite using the commutative property of multiplication.

$- 5 c \cdot c^{3} + c \cdot - 1$

Step 6

Move $- 1$ to the left of $c$ .

$- 5 c \cdot c^{3} - 1 \cdot c$

Step 7

Simplify each term.

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Step 7.1

Multiply $c$ by $c^{3}$ by adding the exponents.

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Step 7.1.1

Move $c^{3}$ .

$- 5 (c^{3} c) - 1 \cdot c$

Step 7.1.2

Multiply $c^{3}$ by $c$ .

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Step 7.1.2.1

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

$- 5 (c^{3} c^{1}) - 1 \cdot c$

Step 7.1.2.2

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

$- 5 c^{3 + 1} - 1 \cdot c$

Step 7.1.3

Add $3$ and $1$ .

$- 5 c^{4} - 1 \cdot c$

Step 7.2

Rewrite $- 1 c$ as $- c$ .

$- 5 c^{4} - c$