Álgebra Exemplos

$\cot^{3} (x) + \cot^{2} (x) + \cot (x) + 1$

Etapa 1

Reagrupe os termos.

$\cot^{3} (x) + 1 + \cot^{2} (x) + \cot (x)$

Etapa 2

Reescreva $1$ como $1^{3}$ .

$\cot^{3} (x) + 1^{3} + \cot^{2} (x) + \cot (x)$

Etapa 3

Como os dois termos são cubos perfeitos, fatore usando a fórmula da soma de cubos, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ em que $a = \cot (x)$ e $b = 1$ .

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

Etapa 4

Simplifique.

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Etapa 4.1

Multiplique $- 1$ por $1$ .

$(\cot (x) + 1) (\cot^{2} (x) - \cot (x) + 1^{2}) + \cot^{2} (x) + \cot (x)$

Etapa 4.2

Um elevado a qualquer potência é um.

$(\cot (x) + 1) (\cot^{2} (x) - \cot (x) + 1) + \cot^{2} (x) + \cot (x)$

Etapa 5

Fatore $\cot (x)$ de $\cot^{2} (x) + \cot (x)$ .

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Etapa 5.1

Fatore $\cot (x)$ de $\cot^{2} (x)$ .

$(\cot (x) + 1) (\cot^{2} (x) - \cot (x) + 1) + \cot (x) \cot (x) + \cot (x)$

Etapa 5.2

Multiplique por $1$ .

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

Etapa 5.3

Fatore $\cot (x)$ de $\cot (x) \cot (x) + \cot (x) \cdot 1$ .

$(\cot (x) + 1) (\cot^{2} (x) - \cot (x) + 1) + \cot (x) (\cot (x) + 1)$

Etapa 6

Fatore $\cot (x) + 1$ de $(\cot (x) + 1) (\cot^{2} (x) - \cot (x) + 1) + \cot (x) (\cot (x) + 1)$ .

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Etapa 6.1

Fatore $\cot (x) + 1$ de $\cot (x) (\cot (x) + 1)$ .

$(\cot (x) + 1) (\cot^{2} (x) - \cot (x) + 1) + (\cot (x) + 1) \cot (x)$

Etapa 6.2

Fatore $\cot (x) + 1$ de $(\cot (x) + 1) (\cot^{2} (x) - \cot (x) + 1) + (\cot (x) + 1) \cot (x)$ .

$(\cot (x) + 1) (\cot^{2} (x) - \cot (x) + 1 + \cot (x))$

Etapa 7

Some $- \cot (x)$ e $\cot (x)$ .

$(\cot (x) + 1) (\cot^{2} (x) + 0 + 1)$

Etapa 8

Some $\cot^{2} (x)$ e $0$ .

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