Основы мат. анализа Примеры

$x^{3} - 216$

Step 1

Rewrite $216$ as $6^{3}$ .

$x^{3} - 6^{3}$

Step 2

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 6$ .

$(x - 6) (x^{2} + x \cdot 6 + 6^{2})$

Step 3

Simplify.

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Step 3.1

Move $6$ to the left of $x$ .

$(x - 6) (x^{2} + 6 x + 6^{2})$

Step 3.2

Raise $6$ to the power of $2$ .

$(x - 6) (x^{2} + 6 x + 36)$

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