Find the Product f(x)=3x-4 , g(x)=9x-6

$f (x) = 3 x - 4$ , $g (x) = 9 x - 6$

Step 1

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

$(3 x - 4) \cdot (9 x - 6)$

Step 2

Simplify.

Expand $(3 x - 4) (9 x - 6)$ using the FOIL Method.

Apply the distributive property.

$3 x (9 x - 6) - 4 (9 x - 6)$

Apply the distributive property.

$3 x (9 x) + 3 x \cdot - 6 - 4 (9 x - 6)$

Apply the distributive property.

$3 x (9 x) + 3 x \cdot - 6 - 4 (9 x) - 4 \cdot - 6$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 9 x \cdot x + 3 x \cdot - 6 - 4 (9 x) - 4 \cdot - 6$

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

Move $x$ .

$3 \cdot 9 (x \cdot x) + 3 x \cdot - 6 - 4 (9 x) - 4 \cdot - 6$

Multiply $x$ by $x$ .

$3 \cdot 9 x^{2} + 3 x \cdot - 6 - 4 (9 x) - 4 \cdot - 6$

Multiply $3$ by $9$ .

$27 x^{2} + 3 x \cdot - 6 - 4 (9 x) - 4 \cdot - 6$

Multiply $- 6$ by $3$ .

$27 x^{2} - 18 x - 4 (9 x) - 4 \cdot - 6$

Multiply $9$ by $- 4$ .

$27 x^{2} - 18 x - 36 x - 4 \cdot - 6$

Multiply $- 4$ by $- 6$ .

$27 x^{2} - 18 x - 36 x + 24$

Subtract $36 x$ from $- 18 x$ .

$27 x^{2} - 54 x + 24$