Pre-Algebra Examples

$- 6 b c^{6} (2 b^{4} - 3 b^{5} c^{2} + 8 c^{2})$

Step 1

Apply the distributive property.

$- 6 b c^{6} (2 b^{4}) - 6 b c^{6} (- 3 b^{5} c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $b^{4}$ .

$- 6 (b^{4} b) c^{6} \cdot 2 - 6 b c^{6} (- 3 b^{5} c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2.1.2

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

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Step 2.1.2.1

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

$- 6 (b^{4} b^{1}) c^{6} \cdot 2 - 6 b c^{6} (- 3 b^{5} c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2.1.2.2

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

$- 6 b^{4 + 1} c^{6} \cdot 2 - 6 b c^{6} (- 3 b^{5} c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2.1.3

Add $4$ and $1$ .

$- 6 b^{5} c^{6} \cdot 2 - 6 b c^{6} (- 3 b^{5} c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2.2

Multiply $b$ by $b^{5}$ by adding the exponents.

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Step 2.2.1

Move $b^{5}$ .

$- 6 b^{5} c^{6} \cdot 2 - 6 (b^{5} b) c^{6} (- 3 c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2.2.2

Multiply $b^{5}$ by $b$ .

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Step 2.2.2.1

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

$- 6 b^{5} c^{6} \cdot 2 - 6 (b^{5} b^{1}) c^{6} (- 3 c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2.2.2.2

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

$- 6 b^{5} c^{6} \cdot 2 - 6 b^{5 + 1} c^{6} (- 3 c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2.2.3

Add $5$ and $1$ .

$- 6 b^{5} c^{6} \cdot 2 - 6 b^{6} c^{6} (- 3 c^{2}) - 6 b c^{6} (8 c^{2})$

Step 2.3

Multiply $c^{6}$ by $c^{2}$ by adding the exponents.

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Step 2.3.1

Move $c^{2}$ .

$- 6 b^{5} c^{6} \cdot 2 - 6 b^{6} c^{6} (- 3 c^{2}) - 6 b (c^{2} c^{6}) \cdot 8$

Step 2.3.2

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

$- 6 b^{5} c^{6} \cdot 2 - 6 b^{6} c^{6} (- 3 c^{2}) - 6 b c^{2 + 6} \cdot 8$

Step 2.3.3

Add $2$ and $6$ .

$- 6 b^{5} c^{6} \cdot 2 - 6 b^{6} c^{6} (- 3 c^{2}) - 6 b c^{8} \cdot 8$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $- 6$ .

$- 12 b^{5} c^{6} - 6 b^{6} c^{6} (- 3 c^{2}) - 6 b c^{8} \cdot 8$

Step 3.2

Multiply $c^{6}$ by $c^{2}$ by adding the exponents.

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Step 3.2.1

Move $c^{2}$ .

$- 12 b^{5} c^{6} - 6 b^{6} (c^{2} c^{6}) \cdot - 3 - 6 b c^{8} \cdot 8$

Step 3.2.2

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

$- 12 b^{5} c^{6} - 6 b^{6} c^{2 + 6} \cdot - 3 - 6 b c^{8} \cdot 8$

Step 3.2.3

Add $2$ and $6$ .

$- 12 b^{5} c^{6} - 6 b^{6} c^{8} \cdot - 3 - 6 b c^{8} \cdot 8$

Step 3.3

Multiply $- 3$ by $- 6$ .

$- 12 b^{5} c^{6} + 18 b^{6} c^{8} - 6 b c^{8} \cdot 8$

Step 3.4

Multiply $8$ by $- 6$ .

$- 12 b^{5} c^{6} + 18 b^{6} c^{8} - 48 b c^{8}$