Evaluate the Function f(x)=(3x+2)(-6x-3)

$f (x) = (3 x + 2) (- 6 x - 3)$

Step 1

Expand $(3 x + 2) (- 6 x - 3)$ using the FOIL Method.

Apply the distributive property.

$f (x) = 3 x (- 6 x - 3) + 2 (- 6 x - 3)$

Apply the distributive property.

$f (x) = 3 x (- 6 x) + 3 x \cdot - 3 + 2 (- 6 x - 3)$

Apply the distributive property.

$f (x) = 3 x (- 6 x) + 3 x \cdot - 3 + 2 (- 6 x) + 2 \cdot - 3$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (x) = 3 \cdot (- 6 x \cdot x) + 3 x \cdot - 3 + 2 (- 6 x) + 2 \cdot - 3$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$f (x) = 3 \cdot (- 6 (x \cdot x)) + 3 x \cdot - 3 + 2 (- 6 x) + 2 \cdot - 3$

Multiply $x$ by $x$ .

$f (x) = 3 \cdot (- 6 x^{2}) + 3 x \cdot - 3 + 2 (- 6 x) + 2 \cdot - 3$

Multiply $3$ by $- 6$ .

$f (x) = - 18 x^{2} + 3 x \cdot - 3 + 2 (- 6 x) + 2 \cdot - 3$

Multiply $- 3$ by $3$ .

$f (x) = - 18 x^{2} - 9 x + 2 (- 6 x) + 2 \cdot - 3$

Multiply $- 6$ by $2$ .

$f (x) = - 18 x^{2} - 9 x - 12 x + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$f (x) = - 18 x^{2} - 9 x - 12 x - 6$

Subtract $12 x$ from $- 9 x$ .

$f (x) = - 18 x^{2} - 21 x - 6$

Step 3