Expand the Trigonometric Expression (3c+2)(c^2-6c-4)

$(3 c + 2) (c^{2} - 6 c - 4)$

Step 1

Expand $(3 c + 2) (c^{2} - 6 c - 4)$ by multiplying each term in the first expression by each term in the second expression.

$3 c \cdot c^{2} + 3 c (- 6 c) + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

Step 2

Simplify terms.

Simplify each term.

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

Move $c^{2}$ .

$3 (c^{2} c) + 3 c (- 6 c) + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

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

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

$3 (c^{2} c^{1}) + 3 c (- 6 c) + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

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

$3 c^{2 + 1} + 3 c (- 6 c) + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

Add $2$ and $1$ .

$3 c^{3} + 3 c (- 6 c) + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

Rewrite using the commutative property of multiplication.

$3 c^{3} + 3 \cdot - 6 c \cdot c + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

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

Move $c$ .

$3 c^{3} + 3 \cdot - 6 (c \cdot c) + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

Multiply $c$ by $c$ .

$3 c^{3} + 3 \cdot - 6 c^{2} + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

Multiply $3$ by $- 6$ .

$3 c^{3} - 18 c^{2} + 3 c \cdot - 4 + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

Multiply $- 4$ by $3$ .

$3 c^{3} - 18 c^{2} - 12 c + 2 c^{2} + 2 (- 6 c) + 2 \cdot - 4$

Multiply $- 6$ by $2$ .

$3 c^{3} - 18 c^{2} - 12 c + 2 c^{2} - 12 c + 2 \cdot - 4$

Multiply $2$ by $- 4$ .

$3 c^{3} - 18 c^{2} - 12 c + 2 c^{2} - 12 c - 8$

Simplify by adding terms.

Add $- 18 c^{2}$ and $2 c^{2}$ .

$3 c^{3} - 16 c^{2} - 12 c - 12 c - 8$

Subtract $12 c$ from $- 12 c$ .

$3 c^{3} - 16 c^{2} - 24 c - 8$