Calculus Examples

${(\tan (θ) - 1)}^{2}$

Rewrite ${(\tan (θ) - 1)}^{2}$ as $(\tan (θ) - 1) (\tan (θ) - 1)$ .

$(\tan (θ) - 1) (\tan (θ) - 1)$

Expand $(\tan (θ) - 1) (\tan (θ) - 1)$ using the FOIL Method.

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Apply the distributive property.

$\tan (θ) (\tan (θ) - 1) - 1 (\tan (θ) - 1)$

Apply the distributive property.

$\tan (θ) \tan (θ) + \tan (θ) \cdot - 1 - 1 (\tan (θ) - 1)$

Apply the distributive property.

$\tan (θ) \tan (θ) + \tan (θ) \cdot - 1 - 1 \tan (θ) - 1 \cdot - 1$

Simplify and combine like terms.

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Simplify each term.

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Multiply $\tan (θ) \tan (θ)$ .

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

$\tan^{1} (θ) \tan (θ) + \tan (θ) \cdot - 1 - 1 \tan (θ) - 1 \cdot - 1$

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

$\tan^{1} (θ) \tan^{1} (θ) + \tan (θ) \cdot - 1 - 1 \tan (θ) - 1 \cdot - 1$

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

${\tan (θ)}^{1 + 1} + \tan (θ) \cdot - 1 - 1 \tan (θ) - 1 \cdot - 1$

Add $1$ and $1$ .

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

Move $- 1$ to the left of $\tan (θ)$ .

$\tan^{2} (θ) - 1 \cdot \tan (θ) - 1 \tan (θ) - 1 \cdot - 1$

Rewrite $- 1 \tan (θ)$ as $- \tan (θ)$ .

$\tan^{2} (θ) - \tan (θ) - 1 \tan (θ) - 1 \cdot - 1$

Rewrite $- 1 \tan (θ)$ as $- \tan (θ)$ .

$\tan^{2} (θ) - \tan (θ) - \tan (θ) - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$\tan^{2} (θ) - \tan (θ) - \tan (θ) + 1$

Subtract $\tan (θ)$ from $- \tan (θ)$ .

$\tan^{2} (θ) - 2 \tan (θ) + 1$