Simplify -6ab^5(a^3b^4-2a^2b-5ab-10)

$- 6 a b^{5} (a^{3} b^{4} - 2 a^{2} b - 5 a b - 10)$

Step 1

Apply the distributive property.

$- 6 a b^{5} (a^{3} b^{4}) - 6 a b^{5} (- 2 a^{2} b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

Step 2

Simplify.

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

Move $a^{3}$ .

$- 6 (a^{3} a) b^{5} b^{4} - 6 a b^{5} (- 2 a^{2} b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

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

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

$- 6 (a^{3} a^{1}) b^{5} b^{4} - 6 a b^{5} (- 2 a^{2} b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

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

$- 6 a^{3 + 1} b^{5} b^{4} - 6 a b^{5} (- 2 a^{2} b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

Add $3$ and $1$ .

$- 6 a^{4} b^{5} b^{4} - 6 a b^{5} (- 2 a^{2} b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

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

Move $a^{2}$ .

$- 6 a^{4} b^{5} b^{4} - 6 (a^{2} a) b^{5} (- 2 b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

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

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

$- 6 a^{4} b^{5} b^{4} - 6 (a^{2} a^{1}) b^{5} (- 2 b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

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

$- 6 a^{4} b^{5} b^{4} - 6 a^{2 + 1} b^{5} (- 2 b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

Add $2$ and $1$ .

$- 6 a^{4} b^{5} b^{4} - 6 a^{3} b^{5} (- 2 b) - 6 a b^{5} (- 5 a b) - 6 a b^{5} \cdot - 10$

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

Move $a$ .

$- 6 a^{4} b^{5} b^{4} - 6 a^{3} b^{5} (- 2 b) - 6 (a \cdot a) b^{5} (- 5 b) - 6 a b^{5} \cdot - 10$

Multiply $a$ by $a$ .

$- 6 a^{4} b^{5} b^{4} - 6 a^{3} b^{5} (- 2 b) - 6 a^{2} b^{5} (- 5 b) - 6 a b^{5} \cdot - 10$

Multiply $- 10$ by $- 6$ .

$- 6 a^{4} b^{5} b^{4} - 6 a^{3} b^{5} (- 2 b) - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

Step 3

Simplify each term.

Multiply $b^{5}$ by $b^{4}$ by adding the exponents.

Move $b^{4}$ .

$- 6 a^{4} (b^{4} b^{5}) - 6 a^{3} b^{5} (- 2 b) - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

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

$- 6 a^{4} b^{4 + 5} - 6 a^{3} b^{5} (- 2 b) - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

Add $4$ and $5$ .

$- 6 a^{4} b^{9} - 6 a^{3} b^{5} (- 2 b) - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

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

Move $b$ .

$- 6 a^{4} b^{9} - 6 a^{3} (b \cdot b^{5}) \cdot - 2 - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

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

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

$- 6 a^{4} b^{9} - 6 a^{3} (b^{1} b^{5}) \cdot - 2 - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

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

$- 6 a^{4} b^{9} - 6 a^{3} b^{1 + 5} \cdot - 2 - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

Add $1$ and $5$ .

$- 6 a^{4} b^{9} - 6 a^{3} b^{6} \cdot - 2 - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

Multiply $- 2$ by $- 6$ .

$- 6 a^{4} b^{9} + 12 a^{3} b^{6} - 6 a^{2} b^{5} (- 5 b) + 60 a b^{5}$

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

Move $b$ .

$- 6 a^{4} b^{9} + 12 a^{3} b^{6} - 6 a^{2} (b \cdot b^{5}) \cdot - 5 + 60 a b^{5}$

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

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

$- 6 a^{4} b^{9} + 12 a^{3} b^{6} - 6 a^{2} (b^{1} b^{5}) \cdot - 5 + 60 a b^{5}$

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

$- 6 a^{4} b^{9} + 12 a^{3} b^{6} - 6 a^{2} b^{1 + 5} \cdot - 5 + 60 a b^{5}$

Add $1$ and $5$ .

$- 6 a^{4} b^{9} + 12 a^{3} b^{6} - 6 a^{2} b^{6} \cdot - 5 + 60 a b^{5}$

Multiply $- 5$ by $- 6$ .

$- 6 a^{4} b^{9} + 12 a^{3} b^{6} + 30 a^{2} b^{6} + 60 a b^{5}$

Simplify -6ab^5(a^3b^4-2a^2b-5ab-10)

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