Evaluate the Function f(x)=(3x+3)(5x-2)

$f (x) = (3 x + 3) (5 x - 2)$

Step 1

Expand $(3 x + 3) (5 x - 2)$ using the FOIL Method.

Apply the distributive property.

$f (x) = 3 x (5 x - 2) + 3 (5 x - 2)$

Apply the distributive property.

$f (x) = 3 x (5 x) + 3 x \cdot - 2 + 3 (5 x - 2)$

Apply the distributive property.

$f (x) = 3 x (5 x) + 3 x \cdot - 2 + 3 (5 x) + 3 \cdot - 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (x) = 3 \cdot (5 x \cdot x) + 3 x \cdot - 2 + 3 (5 x) + 3 \cdot - 2$

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

Move $x$ .

$f (x) = 3 \cdot (5 (x \cdot x)) + 3 x \cdot - 2 + 3 (5 x) + 3 \cdot - 2$

Multiply $x$ by $x$ .

$f (x) = 3 \cdot (5 x^{2}) + 3 x \cdot - 2 + 3 (5 x) + 3 \cdot - 2$

Multiply $3$ by $5$ .

$f (x) = 15 x^{2} + 3 x \cdot - 2 + 3 (5 x) + 3 \cdot - 2$

Multiply $- 2$ by $3$ .

$f (x) = 15 x^{2} - 6 x + 3 (5 x) + 3 \cdot - 2$

Multiply $5$ by $3$ .

$f (x) = 15 x^{2} - 6 x + 15 x + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$f (x) = 15 x^{2} - 6 x + 15 x - 6$

Add $- 6 x$ and $15 x$ .

$f (x) = 15 x^{2} + 9 x - 6$

Step 3