Find the Product f(x)=2x-4 , g(x)=6-x

$f (x) = 2 x - 4$ , $g (x) = 6 - x$

Step 1

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

$(2 x - 4) \cdot (6 - x)$

Step 2

Simplify.

Expand $(2 x - 4) (6 - x)$ using the FOIL Method.

Apply the distributive property.

$2 x (6 - x) - 4 (6 - x)$

Apply the distributive property.

$2 x \cdot 6 + 2 x (- x) - 4 (6 - x)$

Apply the distributive property.

$2 x \cdot 6 + 2 x (- x) - 4 \cdot 6 - 4 (- x)$

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $2$ .

$12 x + 2 x (- x) - 4 \cdot 6 - 4 (- x)$

Rewrite using the commutative property of multiplication.

$12 x + 2 \cdot - 1 x \cdot x - 4 \cdot 6 - 4 (- x)$

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

Move $x$ .

$12 x + 2 \cdot - 1 (x \cdot x) - 4 \cdot 6 - 4 (- x)$

Multiply $x$ by $x$ .

$12 x + 2 \cdot - 1 x^{2} - 4 \cdot 6 - 4 (- x)$

Multiply $2$ by $- 1$ .

$12 x - 2 x^{2} - 4 \cdot 6 - 4 (- x)$

Multiply $- 4$ by $6$ .

$12 x - 2 x^{2} - 24 - 4 (- x)$

Multiply $- 1$ by $- 4$ .

$12 x - 2 x^{2} - 24 + 4 x$

Add $12 x$ and $4 x$ .

$16 x - 2 x^{2} - 24$