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

$f (x) = {(x + 3)}^{2}$

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

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$f (x) = (x + 3) (x + 3)$

Step 3

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

Apply the distributive property.

$f (x) = x (x + 3) + 3 (x + 3)$

Apply the distributive property.

$f (x) = x \cdot x + x \cdot 3 + 3 (x + 3)$

Apply the distributive property.

$f (x) = x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3$

Step 4

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $3$ to the left of $x$ .

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

Multiply $3$ by $3$ .

$f (x) = x^{2} + 3 x + 3 x + 9$

Add $3 x$ and $3 x$ .

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