Simplify (c^2-4)/(c+3)*(3(c^2-9))/(c+2)

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

Step 1

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = c$ and $b = 2$ .

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

Step 2

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = c$ and $b = 3$ .

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

Step 3

Simplify terms.

Cancel the common factor of $c + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $c + 3$ .

Factor $c + 3$ out of $3 (c + 3) (c - 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$(c - 2) \cdot (3 (c - 3))$

Apply the distributive property.

$(c - 2) \cdot (3 c + 3 \cdot - 3)$

Multiply $3$ by $- 3$ .

$(c - 2) \cdot (3 c - 9)$

Step 4

Expand $(c - 2) (3 c - 9)$ using the FOIL Method.

Apply the distributive property.

$c (3 c - 9) - 2 (3 c - 9)$

Apply the distributive property.

$c (3 c) + c \cdot - 9 - 2 (3 c - 9)$

Apply the distributive property.

$c (3 c) + c \cdot - 9 - 2 (3 c) - 2 \cdot - 9$

Step 5

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 c \cdot c + c \cdot - 9 - 2 (3 c) - 2 \cdot - 9$

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

Move $c$ .

$3 (c \cdot c) + c \cdot - 9 - 2 (3 c) - 2 \cdot - 9$

Multiply $c$ by $c$ .

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

Move $- 9$ to the left of $c$ .

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

Multiply $3$ by $- 2$ .

$3 c^{2} - 9 c - 6 c - 2 \cdot - 9$

Multiply $- 2$ by $- 9$ .

$3 c^{2} - 9 c - 6 c + 18$

Subtract $6 c$ from $- 9 c$ .

$3 c^{2} - 15 c + 18$

Simplify (c^2-4)/(c+3)*(3(c^2-9))/(c+2)

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