Find the Product -7c^3d^2(9c^2d^2-4cd^5)

$- 7 c^{3} d^{2} (9 c^{2} d^{2} - 4 c d^{5})$

Apply the distributive property.

$- 7 c^{3} d^{2} (9 c^{2} d^{2}) - 7 c^{3} d^{2} (- 4 c d^{5})$

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

Move $c^{2}$ .

$- 7 (c^{2} c^{3}) d^{2} (9 d^{2}) - 7 c^{3} d^{2} (- 4 c d^{5})$

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

$- 7 c^{2 + 3} d^{2} (9 d^{2}) - 7 c^{3} d^{2} (- 4 c d^{5})$

Add $2$ and $3$ .

$- 7 c^{5} d^{2} (9 d^{2}) - 7 c^{3} d^{2} (- 4 c d^{5})$

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

Move $c$ .

$- 7 c^{5} d^{2} (9 d^{2}) - 7 (c \cdot c^{3}) d^{2} (- 4 d^{5})$

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

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

$- 7 c^{5} d^{2} (9 d^{2}) - 7 (c^{1} c^{3}) d^{2} (- 4 d^{5})$

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

$- 7 c^{5} d^{2} (9 d^{2}) - 7 c^{1 + 3} d^{2} (- 4 d^{5})$

Add $1$ and $3$ .

$- 7 c^{5} d^{2} (9 d^{2}) - 7 c^{4} d^{2} (- 4 d^{5})$

Simplify each term.

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

Move $d^{2}$ .

$- 7 c^{5} (d^{2} d^{2}) \cdot 9 - 7 c^{4} d^{2} (- 4 d^{5})$

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

$- 7 c^{5} d^{2 + 2} \cdot 9 - 7 c^{4} d^{2} (- 4 d^{5})$

Add $2$ and $2$ .

$- 7 c^{5} d^{4} \cdot 9 - 7 c^{4} d^{2} (- 4 d^{5})$

Multiply $9$ by $- 7$ .

$- 63 c^{5} d^{4} - 7 c^{4} d^{2} (- 4 d^{5})$

Multiply $d^{2}$ by $d^{5}$ by adding the exponents.

Move $d^{5}$ .

$- 63 c^{5} d^{4} - 7 c^{4} (d^{5} d^{2}) \cdot - 4$

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

$- 63 c^{5} d^{4} - 7 c^{4} d^{5 + 2} \cdot - 4$

Add $5$ and $2$ .

$- 63 c^{5} d^{4} - 7 c^{4} d^{7} \cdot - 4$

Multiply $- 4$ by $- 7$ .

$- 63 c^{5} d^{4} + 28 c^{4} d^{7}$