Find the Product -4c^2d^3(5cd^2+3c^2d)

$- 4 c^{2} d^{3} (5 c d^{2} + 3 c^{2} d)$

Apply the distributive property.

$- 4 c^{2} d^{3} (5 c d^{2}) - 4 c^{2} d^{3} (3 c^{2} d)$

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

Move $c$ .

$- 4 (c \cdot c^{2}) d^{3} (5 d^{2}) - 4 c^{2} d^{3} (3 c^{2} d)$

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

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

$- 4 (c^{1} c^{2}) d^{3} (5 d^{2}) - 4 c^{2} d^{3} (3 c^{2} d)$

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

$- 4 c^{1 + 2} d^{3} (5 d^{2}) - 4 c^{2} d^{3} (3 c^{2} d)$

Add $1$ and $2$ .

$- 4 c^{3} d^{3} (5 d^{2}) - 4 c^{2} d^{3} (3 c^{2} d)$

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

Move $c^{2}$ .

$- 4 c^{3} d^{3} (5 d^{2}) - 4 (c^{2} c^{2}) d^{3} (3 d)$

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

$- 4 c^{3} d^{3} (5 d^{2}) - 4 c^{2 + 2} d^{3} (3 d)$

Add $2$ and $2$ .

$- 4 c^{3} d^{3} (5 d^{2}) - 4 c^{4} d^{3} (3 d)$

Simplify each term.

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

Move $d^{2}$ .

$- 4 c^{3} (d^{2} d^{3}) \cdot 5 - 4 c^{4} d^{3} (3 d)$

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

$- 4 c^{3} d^{2 + 3} \cdot 5 - 4 c^{4} d^{3} (3 d)$

Add $2$ and $3$ .

$- 4 c^{3} d^{5} \cdot 5 - 4 c^{4} d^{3} (3 d)$

Multiply $5$ by $- 4$ .

$- 20 c^{3} d^{5} - 4 c^{4} d^{3} (3 d)$

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

Move $d$ .

$- 20 c^{3} d^{5} - 4 c^{4} (d \cdot d^{3}) \cdot 3$

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

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

$- 20 c^{3} d^{5} - 4 c^{4} (d^{1} d^{3}) \cdot 3$

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

$- 20 c^{3} d^{5} - 4 c^{4} d^{1 + 3} \cdot 3$

Add $1$ and $3$ .

$- 20 c^{3} d^{5} - 4 c^{4} d^{4} \cdot 3$

Multiply $3$ by $- 4$ .

$- 20 c^{3} d^{5} - 12 c^{4} d^{4}$