Finite Math Examples

$f (x) = 2 - 2 x$ , $g (x) = - 9 x + 2$

Step 1

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

$(2 - 2 x) \cdot (- 9 x + 2)$

Step 2

Simplify.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$2 (- 9 x + 2) - 2 x (- 9 x + 2)$

Step 2.1.2

Apply the distributive property.

$2 (- 9 x) + 2 \cdot 2 - 2 x (- 9 x + 2)$

Step 2.1.3

Apply the distributive property.

$2 (- 9 x) + 2 \cdot 2 - 2 x (- 9 x) - 2 x \cdot 2$

Step 2.2

Simplify and combine like terms.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

Multiply $- 9$ by $2$ .

$- 18 x + 2 \cdot 2 - 2 x (- 9 x) - 2 x \cdot 2$

Step 2.2.1.2

Multiply $2$ by $2$ .

$- 18 x + 4 - 2 x (- 9 x) - 2 x \cdot 2$

Step 2.2.1.3

Rewrite using the commutative property of multiplication.

$- 18 x + 4 - 2 \cdot - 9 x \cdot x - 2 x \cdot 2$

Step 2.2.1.4

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

Tap for more steps...

Step 2.2.1.4.1

Move $x$ .

$- 18 x + 4 - 2 \cdot - 9 (x \cdot x) - 2 x \cdot 2$

Step 2.2.1.4.2

Multiply $x$ by $x$ .

$- 18 x + 4 - 2 \cdot - 9 x^{2} - 2 x \cdot 2$

Step 2.2.1.5

Multiply $- 2$ by $- 9$ .

$- 18 x + 4 + 18 x^{2} - 2 x \cdot 2$

Step 2.2.1.6

Multiply $2$ by $- 2$ .

$- 18 x + 4 + 18 x^{2} - 4 x$

Step 2.2.2

Subtract $4 x$ from $- 18 x$ .

$- 22 x + 4 + 18 x^{2}$