Simplify (1+tan(x))^2

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

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

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

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

Tap for more steps…

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Tap for more steps…

Simplify each term.

Tap for more steps…

Multiply $1$ by $1$ .

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

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

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

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

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

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

Tap for more steps…

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Simplify (1+tan(x))^2

Do you need help with math?