Simplify (c^2-4)(2c+3)

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

Step 1

Expand $(c^{2} - 4) (2 c + 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $c$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Move $3$ to the left of $c^{2}$ .

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

Multiply $2$ by $- 4$ .

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

Multiply $- 4$ by $3$ .

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