Simplify 3c(4c^2-5)-c(9c)

$3 c (4 c^{2} - 5) - c (9 c)$

Step 1

Simplify each term.

Apply the distributive property.

$3 c (4 c^{2}) + 3 c \cdot - 5 - c (9 c)$

Rewrite using the commutative property of multiplication.

$3 \cdot 4 c \cdot c^{2} + 3 c \cdot - 5 - c (9 c)$

Multiply $- 5$ by $3$ .

$3 \cdot 4 c \cdot c^{2} - 15 c - c (9 c)$

Simplify each term.

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

Move $c^{2}$ .

$3 \cdot 4 (c^{2} c) - 15 c - c (9 c)$

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

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

$3 \cdot 4 (c^{2} c^{1}) - 15 c - c (9 c)$

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

$3 \cdot 4 c^{2 + 1} - 15 c - c (9 c)$

Add $2$ and $1$ .

$3 \cdot 4 c^{3} - 15 c - c (9 c)$

Multiply $3$ by $4$ .

$12 c^{3} - 15 c - c (9 c)$

Rewrite using the commutative property of multiplication.

$12 c^{3} - 15 c - 1 \cdot 9 c \cdot c$

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

Move $c$ .

$12 c^{3} - 15 c - 1 \cdot 9 (c \cdot c)$

Multiply $c$ by $c$ .

$12 c^{3} - 15 c - 1 \cdot 9 c^{2}$

Multiply $- 1$ by $9$ .

$12 c^{3} - 15 c - 9 c^{2}$

Step 2

Move $- 15 c$ .

$12 c^{3} - 9 c^{2} - 15 c$