Simplify (tan(x)+1)^2

${(\tan (x) + 1)}^{2}$

Rewrite ${(\tan (x) + 1)}^{2}$ as $(\tan (x) + 1) (\tan (x) + 1)$ .

$(\tan (x) + 1) (\tan (x) + 1)$

Expand $(\tan (x) + 1) (\tan (x) + 1)$ using the FOIL Method.

Apply the distributive property.

$\tan (x) (\tan (x) + 1) + 1 (\tan (x) + 1)$

Apply the distributive property.

$\tan (x) \tan (x) + \tan (x) \cdot 1 + 1 (\tan (x) + 1)$

Apply the distributive property.

$\tan (x) \tan (x) + \tan (x) \cdot 1 + 1 \tan (x) + 1 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Multiply $\tan (x) \tan (x)$ .

Raise $\tan (x)$ to the power of $1$ .

$\tan^{1} (x) \tan (x) + \tan (x) \cdot 1 + 1 \tan (x) + 1 \cdot 1$

Raise $\tan (x)$ to the power of $1$ .

$\tan^{1} (x) \tan^{1} (x) + \tan (x) \cdot 1 + 1 \tan (x) + 1 \cdot 1$

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

${\tan (x)}^{1 + 1} + \tan (x) \cdot 1 + 1 \tan (x) + 1 \cdot 1$

Add $1$ and $1$ .

$\tan^{2} (x) + \tan (x) \cdot 1 + 1 \tan (x) + 1 \cdot 1$

Multiply $\tan (x)$ by $1$ .

$\tan^{2} (x) + \tan (x) + 1 \tan (x) + 1 \cdot 1$

Multiply $\tan (x)$ by $1$ .

$\tan^{2} (x) + \tan (x) + \tan (x) + 1 \cdot 1$

Multiply $1$ by $1$ .

$\tan^{2} (x) + \tan (x) + \tan (x) + 1$

Add $\tan (x)$ and $\tan (x)$ .

$\tan^{2} (x) + 2 \tan (x) + 1$