Simplify -3ab^4(3a^5+7a^3b^2)

$- 3 a b^{4} (3 a^{5} + 7 a^{3} b^{2})$

Step 1

Apply the distributive property.

$- 3 a b^{4} (3 a^{5}) - 3 a b^{4} (7 a^{3} b^{2})$

Step 2

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

Move $a^{5}$ .

$- 3 (a^{5} a) b^{4} \cdot 3 - 3 a b^{4} (7 a^{3} b^{2})$

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

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

$- 3 (a^{5} a^{1}) b^{4} \cdot 3 - 3 a b^{4} (7 a^{3} b^{2})$

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

$- 3 a^{5 + 1} b^{4} \cdot 3 - 3 a b^{4} (7 a^{3} b^{2})$

Add $5$ and $1$ .

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

Step 3

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

Move $a^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Step 4

Simplify each term.

Multiply $3$ by $- 3$ .

$- 9 a^{6} b^{4} - 3 a^{4} b^{4} (7 b^{2})$

Multiply $b^{4}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$- 9 a^{6} b^{4} - 3 a^{4} (b^{2} b^{4}) \cdot 7$

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

$- 9 a^{6} b^{4} - 3 a^{4} b^{2 + 4} \cdot 7$

Add $2$ and $4$ .

$- 9 a^{6} b^{4} - 3 a^{4} b^{6} \cdot 7$

Multiply $7$ by $- 3$ .

$- 9 a^{6} b^{4} - 21 a^{4} b^{6}$