Find the Product 2cd^4(-4c^6d^5-c^3d)

$2 c d^{4} (- 4 c^{6} d^{5} - c^{3} d)$

Step 1

Apply the distributive property.

$2 c d^{4} (- 4 c^{6} d^{5}) + 2 c d^{4} (- c^{3} d)$

Step 2

Multiply $c$ by $c^{6}$ by adding the exponents.

Move $c^{6}$ .

$2 (c^{6} c) d^{4} (- 4 d^{5}) + 2 c d^{4} (- c^{3} d)$

Multiply $c^{6}$ by $c$ .

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

$2 (c^{6} c^{1}) d^{4} (- 4 d^{5}) + 2 c d^{4} (- c^{3} d)$

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

$2 c^{6 + 1} d^{4} (- 4 d^{5}) + 2 c d^{4} (- c^{3} d)$

Add $6$ and $1$ .

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

Step 3

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

Move $c^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Step 4

Simplify each term.

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

Move $d^{5}$ .

$2 c^{7} (d^{5} d^{4}) \cdot - 4 + 2 c^{4} d^{4} (- 1 d)$

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

$2 c^{7} d^{5 + 4} \cdot - 4 + 2 c^{4} d^{4} (- 1 d)$

Add $5$ and $4$ .

$2 c^{7} d^{9} \cdot - 4 + 2 c^{4} d^{4} (- 1 d)$

Multiply $- 4$ by $2$ .

$- 8 c^{7} d^{9} + 2 c^{4} d^{4} (- 1 d)$

Multiply $d^{4}$ by $d$ by adding the exponents.

Move $d$ .

$- 8 c^{7} d^{9} + 2 c^{4} (d \cdot d^{4}) \cdot - 1$

Multiply $d$ by $d^{4}$ .

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

$- 8 c^{7} d^{9} + 2 c^{4} (d^{1} d^{4}) \cdot - 1$

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

$- 8 c^{7} d^{9} + 2 c^{4} d^{1 + 4} \cdot - 1$

Add $1$ and $4$ .

$- 8 c^{7} d^{9} + 2 c^{4} d^{5} \cdot - 1$

Multiply $- 1$ by $2$ .

$- 8 c^{7} d^{9} - 2 c^{4} d^{5}$

Find the Product 2cd^4(-4c^6d^5-c^3d)

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