Precalculus Examples

$f (x) = 5 x^{2} - 8 x$ , $g (x) = x^{2} - 8 x + 16$

Step 1

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

$5 x^{2} - 8 x - (x^{2} - 8 x + 16)$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

$5 x^{2} - 8 x - x^{2} - (- 8 x) - 1 \cdot 16$

Step 2.2

Simplify.

Tap for more steps...

Step 2.2.1

Multiply $- 8$ by $- 1$ .

$5 x^{2} - 8 x - x^{2} + 8 x - 1 \cdot 16$

Step 2.2.2

Multiply $- 1$ by $16$ .

$5 x^{2} - 8 x - x^{2} + 8 x - 16$

Step 3

Simplify by adding terms.

Tap for more steps...

Step 3.1

Combine the opposite terms in $5 x^{2} - 8 x - x^{2} + 8 x - 16$ .

Tap for more steps...

Step 3.1.1

Add $- 8 x$ and $8 x$ .

$5 x^{2} - x^{2} + 0 - 16$

Step 3.1.2

Add $5 x^{2} - x^{2}$ and $0$ .

$5 x^{2} - x^{2} - 16$

Step 3.2

Subtract $x^{2}$ from $5 x^{2}$ .

$4 x^{2} - 16$