Evaluate Using the Given Value f(2)=2(2)^3-(2)^2-5*2+6

$f (2) = 2 {(2)}^{3} - {(2)}^{2} - 5 \cdot 2 + 6$

Step 1

Simplify each term.

Multiply $2$ by ${(2)}^{3}$ by adding the exponents.

Multiply $2$ by ${(2)}^{3}$ .

Raise $2$ to the power of $1$ .

$f (2) = 2 {(2)}^{3} - {(2)}^{2} - 5 \cdot 2 + 6$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (2) = 2^{1 + 3} - {(2)}^{2} - 5 \cdot 2 + 6$

Add $1$ and $3$ .

$f (2) = 2^{4} - {(2)}^{2} - 5 \cdot 2 + 6$

Raise $2$ to the power of $4$ .

$f (2) = 16 - {(2)}^{2} - 5 \cdot 2 + 6$

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

$f (2) = 16 - 1 \cdot 4 - 5 \cdot 2 + 6$

Multiply $- 1$ by $4$ .

$f (2) = 16 - 4 - 5 \cdot 2 + 6$

Multiply $- 5$ by $2$ .

$f (2) = 16 - 4 - 10 + 6$

Step 2

Simplify by adding and subtracting.

Subtract $4$ from $16$ .

$f (2) = 12 - 10 + 6$

Subtract $10$ from $12$ .

$f (2) = 2 + 6$

Add $2$ and $6$ .

$f (2) = 8$