Evaluate the Function g(2+h)=(2+h)^3

$g (2 + h) = {(2 + h)}^{3}$

Use the Binomial Theorem.

$g (2 + h) = 2^{3} + 3 \cdot (2^{2} h) + 3 \cdot (2 h^{2}) + h^{3}$

Simplify each term.

Raise $2$ to the power of $3$ .

$g (2 + h) = 8 + 3 \cdot (2^{2} h) + 3 \cdot (2 h^{2}) + h^{3}$

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

$g (2 + h) = 8 + 3 \cdot (4 h) + 3 \cdot (2 h^{2}) + h^{3}$

Multiply $3$ by $4$ .

$g (2 + h) = 8 + 12 h + 3 \cdot (2 h^{2}) + h^{3}$

Multiply $3$ by $2$ .

$g (2 + h) = 8 + 12 h + 6 h^{2} + h^{3}$