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

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

Rewrite ${(2 + h)}^{2}$ as $(2 + h) (2 + h)$ .

$g (2 + h) = (2 + h) (2 + h)$

Expand $(2 + h) (2 + h)$ using the FOIL Method.

Apply the distributive property.

$g (2 + h) = 2 (2 + h) + h (2 + h)$

Apply the distributive property.

$g (2 + h) = 2 \cdot 2 + 2 h + h (2 + h)$

Apply the distributive property.

$g (2 + h) = 2 \cdot 2 + 2 h + h \cdot 2 + h \cdot h$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$g (2 + h) = 4 + 2 h + h \cdot 2 + h \cdot h$

Move $2$ to the left of $h$ .

$g (2 + h) = 4 + 2 h + 2 \cdot h + h \cdot h$

Multiply $h$ by $h$ .

$g (2 + h) = 4 + 2 h + 2 h + h^{2}$

Add $2 h$ and $2 h$ .

$g (2 + h) = 4 + 4 h + h^{2}$