Simplify -6v^6(3v^3+6v^2-8v)

$- 6 v^{6} (3 v^{3} + 6 v^{2} - 8 v)$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

Multiply

$v^{6}$ by

$v^{3}$ by adding the exponents.

Move

$v^{3}$ .

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

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add

$3$ and

$6$ .

$- 6 \cdot 3 v^{9} - 6 \cdot 6 v^{6} v^{2} - 6 \cdot - 8 v^{6} v$

Multiply

$- 6$ by

$3$ .

$- 18 v^{9} - 6 \cdot 6 v^{6} v^{2} - 6 \cdot - 8 v^{6} v$

Multiply

$v^{6}$ by

$v^{2}$ by adding the exponents.

Move

$v^{2}$ .

$- 18 v^{9} - 6 \cdot 6 (v^{2} v^{6}) - 6 \cdot - 8 v^{6} v$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 18 v^{9} - 6 \cdot 6 v^{2 + 6} - 6 \cdot - 8 v^{6} v$

Add

$2$ and

$6$ .

$- 18 v^{9} - 6 \cdot 6 v^{8} - 6 \cdot - 8 v^{6} v$

Multiply

$- 6$ by

$6$ .

$- 18 v^{9} - 36 v^{8} - 6 \cdot - 8 v^{6} v$

Multiply

$v^{6}$ by

$v$ by adding the exponents.

Move

$v$ .

$- 18 v^{9} - 36 v^{8} - 6 \cdot - 8 (v \cdot v^{6})$

Multiply

$v$ by

$v^{6}$ .

Raise

$v$ to the power of

$1$ .

$- 18 v^{9} - 36 v^{8} - 6 \cdot - 8 (v^{1} v^{6})$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 18 v^{9} - 36 v^{8} - 6 \cdot - 8 v^{1 + 6}$

Add

$1$ and

$6$ .

$- 18 v^{9} - 36 v^{8} - 6 \cdot - 8 v^{7}$

Multiply

$- 6$ by

$- 8$ .

$- 18 v^{9} - 36 v^{8} + 48 v^{7}$

Simplify -6v^6(3v^3+6v^2-8v)

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