Find the Product f(x)=2x+1 , g(x)=3x+9

$f (x) = 2 x + 1$ , $g (x) = 3 x + 9$

Step 1

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

$(2 x + 1) \cdot (3 x + 9)$

Step 2

Simplify.

Expand $(2 x + 1) (3 x + 9)$ using the FOIL Method.

Apply the distributive property.

$2 x (3 x + 9) + 1 (3 x + 9)$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot 9 + 1 (3 x + 9)$

Apply the distributive property.

$2 x (3 x) + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

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

Move $x$ .

$2 \cdot 3 (x \cdot x) + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Multiply $2$ by $3$ .

$6 x^{2} + 2 x \cdot 9 + 1 (3 x) + 1 \cdot 9$

Multiply $9$ by $2$ .

$6 x^{2} + 18 x + 1 (3 x) + 1 \cdot 9$

Multiply $3 x$ by $1$ .

$6 x^{2} + 18 x + 3 x + 1 \cdot 9$

Multiply $9$ by $1$ .

$6 x^{2} + 18 x + 3 x + 9$

Add $18 x$ and $3 x$ .

$6 x^{2} + 21 x + 9$