Simplify c^2d^3(5cd^7-3c^3d^2-4d^3)

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

Apply the distributive property.

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

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Simplify each term.

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

Move $c$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $d^{3}$ by $d^{7}$ by adding the exponents.

Move $d^{7}$ .

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

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

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

Add $7$ and $3$ .

$5 c^{3} d^{10} - 3 c^{2} d^{3} (c^{3} d^{2}) - 4 c^{2} d^{3} d^{3}$

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

Move $c^{3}$ .

$5 c^{3} d^{10} - 3 (c^{3} c^{2}) d^{3} d^{2} - 4 c^{2} d^{3} d^{3}$

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

$5 c^{3} d^{10} - 3 c^{3 + 2} d^{3} d^{2} - 4 c^{2} d^{3} d^{3}$

Add $3$ and $2$ .

$5 c^{3} d^{10} - 3 c^{5} d^{3} d^{2} - 4 c^{2} d^{3} d^{3}$

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

Move $d^{2}$ .

$5 c^{3} d^{10} - 3 c^{5} (d^{2} d^{3}) - 4 c^{2} d^{3} d^{3}$

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

$5 c^{3} d^{10} - 3 c^{5} d^{2 + 3} - 4 c^{2} d^{3} d^{3}$

Add $2$ and $3$ .

$5 c^{3} d^{10} - 3 c^{5} d^{5} - 4 c^{2} d^{3} d^{3}$

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

Move $d^{3}$ .

$5 c^{3} d^{10} - 3 c^{5} d^{5} - 4 c^{2} (d^{3} d^{3})$

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

$5 c^{3} d^{10} - 3 c^{5} d^{5} - 4 c^{2} d^{3 + 3}$

Add $3$ and $3$ .

$5 c^{3} d^{10} - 3 c^{5} d^{5} - 4 c^{2} d^{6}$

Simplify c^2d^3(5cd^7-3c^3d^2-4d^3)

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