Simplify -8ab^3(a^5b^4+6a^2b+3ab-6)

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

Apply the distributive property.

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

Simplify.

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

Move $a^{5}$ .

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

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

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

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

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

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

Add $5$ and $1$ .

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

Multiply $a$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

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

Multiply $a^{2}$ by $a$ .

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

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

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

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

Add $2$ and $1$ .

$- 8 a^{6} b^{3} b^{4} - 8 a^{3} b^{3} (6 b) - 8 a b^{3} (3 a b) - 8 a b^{3} \cdot - 6$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$- 8 a^{6} b^{3} b^{4} - 8 a^{3} b^{3} (6 b) - 8 (a \cdot a) b^{3} (3 b) - 8 a b^{3} \cdot - 6$

Multiply $a$ by $a$ .

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

Multiply $- 6$ by $- 8$ .

$- 8 a^{6} b^{3} b^{4} - 8 a^{3} b^{3} (6 b) - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

Simplify each term.

Multiply $b^{3}$ by $b^{4}$ by adding the exponents.

Move $b^{4}$ .

$- 8 a^{6} (b^{4} b^{3}) - 8 a^{3} b^{3} (6 b) - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

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

$- 8 a^{6} b^{4 + 3} - 8 a^{3} b^{3} (6 b) - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

Add $4$ and $3$ .

$- 8 a^{6} b^{7} - 8 a^{3} b^{3} (6 b) - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

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

Move $b$ .

$- 8 a^{6} b^{7} - 8 a^{3} (b \cdot b^{3}) \cdot 6 - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

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

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

$- 8 a^{6} b^{7} - 8 a^{3} (b^{1} b^{3}) \cdot 6 - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

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

$- 8 a^{6} b^{7} - 8 a^{3} b^{1 + 3} \cdot 6 - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

Add $1$ and $3$ .

$- 8 a^{6} b^{7} - 8 a^{3} b^{4} \cdot 6 - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

Multiply $6$ by $- 8$ .

$- 8 a^{6} b^{7} - 48 a^{3} b^{4} - 8 a^{2} b^{3} (3 b) + 48 a b^{3}$

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

Move $b$ .

$- 8 a^{6} b^{7} - 48 a^{3} b^{4} - 8 a^{2} (b \cdot b^{3}) \cdot 3 + 48 a b^{3}$

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

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

$- 8 a^{6} b^{7} - 48 a^{3} b^{4} - 8 a^{2} (b^{1} b^{3}) \cdot 3 + 48 a b^{3}$

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

$- 8 a^{6} b^{7} - 48 a^{3} b^{4} - 8 a^{2} b^{1 + 3} \cdot 3 + 48 a b^{3}$

Add $1$ and $3$ .

$- 8 a^{6} b^{7} - 48 a^{3} b^{4} - 8 a^{2} b^{4} \cdot 3 + 48 a b^{3}$

Multiply $3$ by $- 8$ .

$- 8 a^{6} b^{7} - 48 a^{3} b^{4} - 24 a^{2} b^{4} + 48 a b^{3}$

Simplify -8ab^3(a^5b^4+6a^2b+3ab-6)

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