Simplify -8c^3(3c^2+2c-9)

$- 8 c^{3} (3 c^{2} + 2 c - 9)$

Step 1

Apply the distributive property.

$- 8 c^{3} (3 c^{2}) - 8 c^{3} (2 c) - 8 c^{3} \cdot - 9$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 8 \cdot 3 c^{3} c^{2} - 8 c^{3} (2 c) - 8 c^{3} \cdot - 9$

Rewrite using the commutative property of multiplication.

$- 8 \cdot 3 c^{3} c^{2} - 8 \cdot 2 c^{3} c - 8 c^{3} \cdot - 9$

Multiply $- 9$ by $- 8$ .

$- 8 \cdot 3 c^{3} c^{2} - 8 \cdot 2 c^{3} c + 72 c^{3}$

Step 3

Simplify each term.

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

Move $c^{2}$ .

$- 8 \cdot 3 (c^{2} c^{3}) - 8 \cdot 2 c^{3} c + 72 c^{3}$

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

$- 8 \cdot 3 c^{2 + 3} - 8 \cdot 2 c^{3} c + 72 c^{3}$

Add $2$ and $3$ .

$- 8 \cdot 3 c^{5} - 8 \cdot 2 c^{3} c + 72 c^{3}$

Multiply $- 8$ by $3$ .

$- 24 c^{5} - 8 \cdot 2 c^{3} c + 72 c^{3}$

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

Move $c$ .

$- 24 c^{5} - 8 \cdot 2 (c \cdot c^{3}) + 72 c^{3}$

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

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

$- 24 c^{5} - 8 \cdot 2 (c^{1} c^{3}) + 72 c^{3}$

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

$- 24 c^{5} - 8 \cdot 2 c^{1 + 3} + 72 c^{3}$

Add $1$ and $3$ .

$- 24 c^{5} - 8 \cdot 2 c^{4} + 72 c^{3}$

Multiply $- 8$ by $2$ .

$- 24 c^{5} - 16 c^{4} + 72 c^{3}$