Write in Standard Form f(x)=3(x-6)(x+2)

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$f (x) = a x^{2} + b x + c$

Step 2

Simplify by multiplying through.

Apply the distributive property.

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

Multiply $3$ by $- 6$ .

$f (x) = (3 x - 18) (x + 2)$

Step 3

Expand $(3 x - 18) (x + 2)$ using the FOIL Method.

Apply the distributive property.

$f (x) = 3 x (x + 2) - 18 (x + 2)$

Apply the distributive property.

$f (x) = 3 x \cdot x + 3 x \cdot 2 - 18 (x + 2)$

Apply the distributive property.

$f (x) = 3 x \cdot x + 3 x \cdot 2 - 18 x - 18 \cdot 2$

Step 4

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$f (x) = 3 (x \cdot x) + 3 x \cdot 2 - 18 x - 18 \cdot 2$

Multiply $x$ by $x$ .

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

Multiply $2$ by $3$ .

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

Multiply $- 18$ by $2$ .

$f (x) = 3 x^{2} + 6 x - 18 x - 36$

Subtract $18 x$ from $6 x$ .

$f (x) = 3 x^{2} - 12 x - 36$