Основы мат. анализа Примеры

$x^{3} + 64$

Step 1

Rewrite $64$ as $4^{3}$ .

$x^{3} + 4^{3}$

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = x$ and $b = 4$ .

$(x + 4) (x^{2} - x \cdot 4 + 4^{2})$

Step 3

Simplify.

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Step 3.1

Multiply $4$ by $- 1$ .

$(x + 4) (x^{2} - 4 x + 4^{2})$

Step 3.2

Raise $4$ to the power of $2$ .

$(x + 4) (x^{2} - 4 x + 16)$

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