Simplify c^3d^2(c^2d-2d)

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

Step 1

Apply the distributive property.

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

Step 2

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

Move $c^{2}$ .

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

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

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

Add $2$ and $3$ .

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

Step 3

Rewrite using the commutative property of multiplication.

$c^{5} d^{2} d - 2 c^{3} d^{2} d$

Step 4

Simplify each term.

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

Move $d$ .

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

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

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

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

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

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

Add $1$ and $2$ .

$c^{5} d^{3} - 2 c^{3} d^{2} d$

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

Move $d$ .

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

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

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

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

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

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

Add $1$ and $2$ .

$c^{5} d^{3} - 2 c^{3} d^{3}$