Trigonometry Examples

x^{3} + 1

$x^{3} + 1$

Step 1

Rewrite

1

$1$ as

1^{3}

$1^{3}$ .

x^{3} + 1^{3}

$x^{3} + 1^{3}$

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula,

a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where

a = x

$a = x$ and

b = 1

$b = 1$ .

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

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

Step 3

Simplify.

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Step 3.1

Multiply

- 1

$- 1$ by

1

$1$ .

(x + 1) (x^{2} - x + 1^{2})

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

Step 3.2

One to any power is one.

(x + 1) (x^{2} - x + 1)

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

(x + 1) (x^{2} - x + 1)

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

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