Simplify 2cd^3(c-d+5)

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

Apply the distributive property.

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

Simplify.

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

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

Multiply $c$ by $c$ .

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

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

Move $d$ .

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

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

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

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

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

$2 c^{2} d^{3} + 2 c d^{1 + 3} \cdot - 1 + 2 c d^{3} \cdot 5$

Add $1$ and $3$ .

$2 c^{2} d^{3} + 2 c d^{4} \cdot - 1 + 2 c d^{3} \cdot 5$

Multiply $5$ by $2$ .

$2 c^{2} d^{3} + 2 c d^{4} \cdot - 1 + 10 c d^{3}$

Multiply $- 1$ by $2$ .

$2 c^{2} d^{3} - 2 c d^{4} + 10 c d^{3}$