Evaluate (1+h)^2

${(1 + h)}^{2}$

Step 1

Rewrite ${(1 + h)}^{2}$ as $(1 + h) (1 + h)$ .

$(1 + h) (1 + h)$

Step 2

Expand $(1 + h) (1 + h)$ using the FOIL Method.

Apply the distributive property.

$1 (1 + h) + h (1 + h)$

Apply the distributive property.

$1 \cdot 1 + 1 h + h (1 + h)$

Apply the distributive property.

$1 \cdot 1 + 1 h + h \cdot 1 + h \cdot h$

$1 \cdot 1 + 1 h + h \cdot 1 + h \cdot h$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$1 + 1 h + h \cdot 1 + h \cdot h$

Multiply $h$ by $1$ .

$1 + h + h \cdot 1 + h \cdot h$

Multiply $h$ by $1$ .

$1 + h + h + h \cdot h$

Multiply $h$ by $h$ .

$1 + h + h + h^{2}$

$1 + h + h + h^{2}$

Add $h$ and $h$ .

$1 + 2 h + h^{2}$

$1 + 2 h + h^{2}$

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