Basic Math Examples

$- 6 y^{3} (2 y^{3} - 3 y^{2} - 8 y)$

Step 1

Apply the distributive property.

$- 6 y^{3} (2 y^{3}) - 6 y^{3} (- 3 y^{2}) - 6 y^{3} (- 8 y)$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 6 \cdot 2 y^{3} y^{3} - 6 y^{3} (- 3 y^{2}) - 6 y^{3} (- 8 y)$

Step 2.2

Rewrite using the commutative property of multiplication.

$- 6 \cdot 2 y^{3} y^{3} - 6 \cdot - 3 y^{3} y^{2} - 6 y^{3} (- 8 y)$

Step 2.3

Rewrite using the commutative property of multiplication.

$- 6 \cdot 2 y^{3} y^{3} - 6 \cdot - 3 y^{3} y^{2} - 6 \cdot - 8 y^{3} y$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $y^{3}$ .

$- 6 \cdot 2 (y^{3} y^{3}) - 6 \cdot - 3 y^{3} y^{2} - 6 \cdot - 8 y^{3} y$

Step 3.1.2

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

$- 6 \cdot 2 y^{3 + 3} - 6 \cdot - 3 y^{3} y^{2} - 6 \cdot - 8 y^{3} y$

Step 3.1.3

Add $3$ and $3$ .

$- 6 \cdot 2 y^{6} - 6 \cdot - 3 y^{3} y^{2} - 6 \cdot - 8 y^{3} y$

Step 3.2

Multiply $- 6$ by $2$ .

$- 12 y^{6} - 6 \cdot - 3 y^{3} y^{2} - 6 \cdot - 8 y^{3} y$

Step 3.3

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

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Step 3.3.1

Move $y^{2}$ .

$- 12 y^{6} - 6 \cdot - 3 (y^{2} y^{3}) - 6 \cdot - 8 y^{3} y$

Step 3.3.2

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

$- 12 y^{6} - 6 \cdot - 3 y^{2 + 3} - 6 \cdot - 8 y^{3} y$

Step 3.3.3

Add $2$ and $3$ .

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

Step 3.4

Multiply $- 6$ by $- 3$ .

$- 12 y^{6} + 18 y^{5} - 6 \cdot - 8 y^{3} y$

Step 3.5

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

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Step 3.5.1

Move $y$ .

$- 12 y^{6} + 18 y^{5} - 6 \cdot - 8 (y \cdot y^{3})$

Step 3.5.2

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

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Step 3.5.2.1

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

$- 12 y^{6} + 18 y^{5} - 6 \cdot - 8 (y^{1} y^{3})$

Step 3.5.2.2

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

$- 12 y^{6} + 18 y^{5} - 6 \cdot - 8 y^{1 + 3}$

Step 3.5.3

Add $1$ and $3$ .

$- 12 y^{6} + 18 y^{5} - 6 \cdot - 8 y^{4}$

Step 3.6

Multiply $- 6$ by $- 8$ .

$- 12 y^{6} + 18 y^{5} + 48 y^{4}$