Algebra Examples

$f (x) = 8 - 10 x$ , $g (x) = 5 x + 4$ , $(f g) (- 2)$

Step 1

Evaluate $f g$ .

Tap for more steps...

Step 1.1

Replace the function designators in $f g$ with the actual functions.

$(8 - 10 x) (5 x + 4)$

Step 1.2

Expand $(8 - 10 x) (5 x + 4)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$8 (5 x + 4) - 10 x (5 x + 4)$

Step 1.2.2

Apply the distributive property.

$8 (5 x) + 8 \cdot 4 - 10 x (5 x + 4)$

Step 1.2.3

Apply the distributive property.

$8 (5 x) + 8 \cdot 4 - 10 x (5 x) - 10 x \cdot 4$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $5$ by $8$ .

$40 x + 8 \cdot 4 - 10 x (5 x) - 10 x \cdot 4$

Step 1.3.1.2

Multiply $8$ by $4$ .

$40 x + 32 - 10 x (5 x) - 10 x \cdot 4$

Step 1.3.1.3

Rewrite using the commutative property of multiplication.

$40 x + 32 - 10 \cdot 5 x \cdot x - 10 x \cdot 4$

Step 1.3.1.4

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

Tap for more steps...

Step 1.3.1.4.1

Move $x$ .

$40 x + 32 - 10 \cdot 5 (x \cdot x) - 10 x \cdot 4$

Step 1.3.1.4.2

Multiply $x$ by $x$ .

$40 x + 32 - 10 \cdot 5 x^{2} - 10 x \cdot 4$

Step 1.3.1.5

Multiply $- 10$ by $5$ .

$40 x + 32 - 50 x^{2} - 10 x \cdot 4$

Step 1.3.1.6

Multiply $4$ by $- 10$ .

$40 x + 32 - 50 x^{2} - 40 x$

Step 1.3.2

Subtract $40 x$ from $40 x$ .

$32 - 50 x^{2} + 0$

Step 1.3.3

Add $32$ and $0$ .

$- 50 x^{2} + 32$

Step 2

Evaluate $f g$ at $- 2$ .

$- 50 {(- 2)}^{2} + 32$

Step 3

Simplify $- 50 {(- 2)}^{2} + 32$ .

Tap for more steps...

Step 3.1

Remove parentheses.

$- 50 {(- 2)}^{2} + 32$

Step 3.2

Simplify each term.

Tap for more steps...

Step 3.2.1

Raise $- 2$ to the power of $2$ .

$- 50 \cdot 4 + 32$

Step 3.2.2

Multiply $- 50$ by $4$ .

$- 200 + 32$

Step 3.3

Add $- 200$ and $32$ .

$- 168$